Volume 2, Number 5
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- September 7, 1995 -
- O P - S F N E T Volume 2, Number 5 -
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- Tom H. Koornwinder, Editor thk@fwi.uva.nl -
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- The Electronic News Net of the SIAM Activity Group -
- on Orthogonal Polynomials and Special Functions -
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- Please send contributions to: poly@siam.org -
- & address changes to: poly-request@siam.org -
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Today's Topics:
1. Newsletter will appear again
2. Election of new officers
3. Problems in getting subscribed to OP-SF Net
4. Minisymposium at SIAM Annual Meeting in Charlotte
5. International Conference on Harmonic Analysis, Delhi, India
6. Report on conference in honour of Lee Lorch
7. Macdonald-Stanley conjecture for Jack polynomials solved (weakly)
8. Death of S. Chandrasekhar
9. Szego bust
10. Proceedings of hypergroups conference
11. New book on Heun's differential equations
12. Early history of Bessel functions
13. Tenure track position in Bogota (Columbia)
14. Looking for a position
15. ftp and WWW addresses
16. Changes of address
17. Obtaining back issues of OP-SF Net
Calendar of events: see issue/topic:
1995
October 25: Minisymposium at SIAM Annual Meeting in Charlotte 2.5 #4
November 27- December 1: main topic q-special functions in fourth week
of Warsaw Minisemester on Quantum groups and quantum spaces: 2.4 #4
December 18-22: International Conference on Harmonic Analysis, Delhi 2.5 #5
1996
April 22-23: Umbral Calculus Special Session at MIT 2.4 #5
May 6-26: CRM Workshop on the Theory of Special Functions 2.1 #5
July 1-5: Meeting in Canterbury on Symmetries and Integrability of
Difference Equations 2.4 #6
August, last week: Workshop Transform Methods & Special Functions 2.4 #7
Topic #1 --------------- OP-SF NET --------------- September 7, 1995
From: OP-SF Net editor <thk@fwi.uva.nl>
Subject: Newsletter will appear again
As already announced in OP-SF Net 2.4, Topic #1, Wolfram Koepf is the
new editor of the printed Newsletter of our Activity Group. The
Newsletter will appear every four months, in October 1995 (submission
deadline September 15) and in February and June 1996. Wolfram Koepf
welcomes Newsletter contributions, preferably by email and in Latex
format. Other formats are also acceptable and can be submitted by
email, regular mail or fax. The editor's address is:
Wolfram Koepf
Konrad-Zuse-Zentrum
Heilbronner Str. 10,
D-10711 Berlin, Germany
tel.: +49-30-896 04-216
fax: +49-30-896 04-125,
email: koepf@zib-berlin.de
Topic #2 --------------- OP-SF NET --------------- September 7, 1995
From: Charles F. Dunkl <cfd5z@fermi.clas.virginia.edu>
Subject: Election of new officers
Members of the Activity group will soon receive ballot forms for
election of new officers of our Activity Group. The candidates are:
chair: Charles Dunkl, unopposed
vice-chair: Tom Koornwinder, unopposed
secretary: Daniel Lozier and Nico Temme
program chair: Willard Miller, Jr. and Alan Schwartz
Topic #3 --------------- OP-SF NET --------------- September 7, 1995
From: OP-SF Net editor <thk@fwi.uva.nl>
Subject: Problems in getting subscribed to OP-SF Net
There have been some complaints in the past from people subscribing
to OP-SF Net and getting no reply. SIAM is working on a new procedure
for handling requests for subscription. In the meantime, if anyone
has complaints, please contact Diane Fryer <fryer@siam.org> at SIAM
or me <thk@fwi.uva.nl>.
Topic #4 --------------- OP-SF NET --------------- September 7, 1995
From: Martin Muldoon (Program Director) <muldoon@mathstat.yorku.ca>
Subject: Minisymposium at SIAM Annual Meeting in Charlotte
We remind you (see OP-SF Net 2.3, Topic #8) that our Activity Group
will sponsor a Minisymposium "Computational Aspects of Special
Functions and Orthogonal Polynomials" at the SIAM Annual Meeting in
Charlotte, North Carolina, October 23-26, 1995. The Minisymposium
will take place on Wednesday, October 25, 5.00-7.30 p.m. The
organizer is Martin E. Muldoon (York University, Canada).
The program is as follows:
5.00 John P. Boyd (University of Michigan, Ann Arbor, MI),
"Numerical verification of exponential asymptotics via a
Chebyshev polynomial pseudospectral algorithm in multiple
precision: radiation coefficient of a weakly nonlocal solitary wave"
5.30 Charles F. Dunkl (University of Virginia, Charlottesville, VA),
"Hyperelliptic integrals, the surface measure of ellipsoids, and
response surfaces" (with Donald E. Ramirez)
6.00 Walter Gautschi (Purdue University, West Lafayette, IN),
"Computing orthogonal polynomials of Sobolev type"
6.30 Daniel W. Lozier (National Institute of Standards and Technology,
Gaithersburg, MD),
"Software issues in the computation of special functions"
7.00 Nico M. Temme (CWI, Amsterdam),
"Large parameter evaluations of some classical distribution functions"
For registration, see the Preliminary Program of the SIAM Annual Meeting
sent to all SIAM members, or see
WWW: http://www.siam.org
or send an email to meeting@siam.org
Topic #5 --------------- OP-SF NET --------------- September 7, 1995
From: A.I. Singh
Subject: International Conference on Harmonic Analysis, Delhi, India
An International Conference on Harmonic Analysis will be organized at
the Department of Mathematics, University of Delhi, Delhi-110007,
India from 18th to 22nd December, 1995. The programme will include
special talks on different aspects of harmonic analysis such as
measure algebras, homomorphisms, multipliers, positive definite
functions, spectral synthesis and H-spaces. A series of expository
lectures on Hypergroups by Professors K.A. Ross, A.L. Schwartz and
others will be a special feature of the conference.
For further information please contact:
Prof.(Mrs> Ajit Iqbal Singh
Department of Mathematics
University of Delhi
Delhi-7, India
fax: +91-11-725 7011
Topic #6 --------------- OP-SF NET --------------- September 7, 1995
From: Walter Van Assche <Walter.VanAssche@wis.kuleuven.ac.be>
Subject: Report on conference in honour of Lee Lorch
(A slightly longer report by Walter Van Assche will appear in the
Newsletter)
In September 1995, Lee Lorch will celebrate his eightieth birthday.
For this occasion, a conference was organized at York University
(Canada) on June 9 and 10, 1995. Some forty people were present and
attended various talks on mathematical topics of interest to Lee
Lorch, but also talks related to the societal topics in which Lee
always has had active interest.
One of Lee's mathematical interests has been the monotonicity
properties of zeros of Bessel functions or functions of a similar
nature. A basic method for studying monotonicity properties of zeros
of special functions is Sturm's method, for which there is a
continuous version (for zeros of the solution of a Sturm-Liouville
differential operator) and there is also a discrete version for
polynomials which form a Sturm sequence (a three-term recurrence with
a particular sign property). Lee Lorch's main contributions can be
found in joint papers with Peter Szego and Martin Muldoon. Lee also
had an continuing interest in Lebesgue constants and various methods
of summability.
On the first day of the conference (June 9, 1995) there were one hour
talks by Richard Askey on "Bessel functions and how to use them when
considering more general classes of functions" and Cora Sadosky on
"Restricted BMO in products spaces". There were also some 30 minute
talks by P.G. Rooney, Walter Van Assche, Angelo Mingarelli, A. McD.
Mercer, Mark Ashbaugh, Mourad Ismail, James A. Donaldson, and Arpad
Elbert dealing with Hankel transforms, zeros of orthogonal
polynomials, eigenvalues of matrices and differential operators,
Bessel functions and isoperimetric inequalities, integral operators
and $q$-Sturm-Liouville problems, and linear shallow water theory.
The morning of the second day of the conference was still devoted to
mathematics with one hour talks by Roderick Wong on "Asymptotics and
special functions", Jean-Pierre Kahane on "Summability, order and
products of Dirichlet series", and 30 minute talks by Dennis Russell
and Mark Pinsky on Fourier transforms and Fourier integrals in several
variables. In the afternoon there was a nice talk by Donald J. Newman
with a beautiful proof of the Morley triangle theorem:
Let ABC be an arbitrary triangle with vertices at the points A, B, C.
Construct a new triangle (the Morley triangle) by trisecting the
angles alpha, beta and gamma at respectively A, B and C inside the
triangle ABC and by taking the first intersection points as the
vertices of the new triangle. Then this Morley triangle is always an
equilateral triangle.
There was also a 30 minute talk by Amram Meir on random trees, and the
rest of the afternoon of June 10 was devoted to Lee's societal
contributions for which he has become well-known, with talks by
Chandler Davis, Mary Gray, and Johnny Houston pointing out the
"Contributions of Lee Lorch to expanding access to mathematics",
showing that Lee Lorch is "A mathematician who cares".
Finally, the conference was closed with a dinner during which Lee was
awarded the Lifetime Achievement Award of the National Association
of Mathematicians by Jack Alexander, president of the Association.
Topic #7 --------------- OP-SF NET --------------- September 7, 1995
From; OP-SF Net editor <thk@fwi.uva.nl>
Subject: Macdonald-Stanley conjecture for Jack polynomials solved (weakly)
This item is partially based on email communications by Doron Zeilberger
<zeilberg@euclid.math.temple.edu> and by Luc Vinet <vinet@ere.umontreal.ca>.
Many conjectures involving the Jack polynomials have been formulated.
A famous one is due to I.G. Macdonald and is reproduced in R.P.
Stanley's reference article "Some combinatorial properties of Jack
symmetric functions, Adv. in Math. 77 (1988), 76-115. Roughly, it
states the following. Let J_lambda(x;alpha) be the Jack polynomial in
the variables x=(x_1,...,x_n) and with parameter alpha. Let the
v_{lambda,mu} be its expansion coefficients in terms of the symmetric
monomials m_mu(x). It is conjectured that these expansion coefficients,
when suitably normalized, are polynomials in alpha with nonnegative
integer coefficients.
Recently, Luc Lapointe and Luc Vinet proved a weak form of the
Macdonald-Stanley conjecture: the suitably normalized coefficients are
polynomials in alpha with integer coefficients. They obtained this result
by first deriving a Rodrigues type formula for the Jack polynomials. This
Rodrigues type formula involves so-called creation operators which are
built from Dunkl operators.
The full proof of the Rodrigues type formula is given in:
L. Lapointe & L. Vinet, Exact operator solution of the Calogero-Sutherland
model, CRM preprint #2272, electronically available as q-alg 9509003
or from WWW: http://www.crm.umontreal.ca
A brief announcement of the Rodrigues type formula together with a proof
of the weak form of the Macdonald-Stanley conjecture is given in:
L. Lapointe & L. Vinet, A Rodrigues formula for the Jack polynomials
and the Macdonald-Stanley conjecture, CRM preprint #2294, electronically
available as q-alg 9509002 or from WWW: http://www.crm.umontreal.ca
This paper will appear soon in the International Mathematics Research
Notices.
To see the Lapointe-Vinet proof in action see Doron Zeilberger's
Maple program LUC, obtainable from
WWW: http://www.math.temple.edu/~zeilberg
Doron Zeilberger adds that he has further news from Adriano Garsia:
Garsia can prove a similar polynomiality conjecture for the Macdonald
polynomials associated with root system A_n.
Topic #8 --------------- OP-SF NET --------------- September 7, 1995
From: OP-SF Net editor <thk@fwi.uva.nl>
Subject: Death of S. Chandrasekhar
(With thanks to Dick Askey, Willard Miller and Ernie Kalnins for providing
information)
Prof. S. Chandrasekhar died on August 22, 1995 at the age of 84. He
was born in Lahore, India and he studied at the University of Madras,
India and at Trinity College, Cambridge, England. He worked at the
University of Chicago. He is well known for his work in theoretical
astronomy, see for instance his book "The mathematical theory of black
holes", Oxford University Press, 1983.
This book left unanswered questions about the intrinsic
characterisation of the explicit solutions of the spinor equations of
mathematical physics in the curved background of a rotating black hole
(Kerr space time). In this problem the so called Teukolsky functions
play a crucial role. These functions are confluent forms of the
solutions of the most general linear homogeneous ordinary differential
equation of second order with four regular singularities, viz. Heun's
equation. Significant progress in the solution of this problem was
made by E.G. Kalnins, W. Miller, Jr., and G.C. Williams.
This summer Chandrasekhar's last book appeared, "Newton's `Principia'
for the common reader", Oxford University Press, 1995. Further
information on his life can be found in the biography "Chandra" by
Kameshwar C. Wali, University of Chicago Press, 1991.
Topic #9 --------------- OP-SF NET --------------- September 7, 1995
From: Paul Nevai <nevai@math.ohio-state.edu>
Subject: Szego bust
The dedication of the Szego bust (see OP-SF Net 2.2, Topic #8) took
place on Wednesday, August 23, 1995, in Kunhegyes, Hungary, in front
of roughly a hundred people, including about 30 mathematicians +
Veronica & Steve Tincher (Szego's daughter and grandson). I like the
statue (bust + pedestal) a lot. The dedication ceremony was very
nicely done. The additional two copies will be done by the end of
September. Thanks again to all who generously supported this project.
(A longer account of this ceremony, written by Kathy A. Driver and
edited by Paul Nevai, is available from Paul Nevai
<nevai@math.ohio-state.edu> on request.)
Topic #10 --------------- OP-SF NET --------------- September 7, 1995
From: OP-SF Net editor <thk@fwi.uva.nl>
Subject: Proceedings of hypergroups conference
The following book was already briefly mentioned in OP-SF Net 2.3,
Topic #14.
Applications of Hypergroups and Related Measure Algebras
William C. Connett, Marc-Olivier Gebuhrer, and Alan L. Schwartz (eds.)
Contemporary Mathematics, 183
American Mathematical Society, 1995
441 pages (softcover)
ISBN 0-8218-0297-6
About the conference:
The most important single thing about this conference was that it
brought together for the first time representatives of all major
groups of users of hypergroups. They talked to each other about how
they were using hypergroups in fields as diverse as special functions,
probability theory, representation theory, measure algebras, Hopf
algebras, and Hecke algebras. This led to fireworks.
About the proceedings:
Hypergroups occur in a wide variety of contexts, and
mathematicians the world over have been discovering this same
mathematical structure hidden in very different applications. The
diverse viewpoints on the subject have led to the need for a common
perspective, if not a common theory. Presenting the proceedings of a
Joint Summer Research Conference held in Seattle in the summer of
1993, this book will serve as a valuable starting point and reference
tool for the wide range of users of hypergroups and make it easier for
an even larger audience to use these structures in their work.
Contents:
N. Ben Salem and M.N. Lazhari, Limit theorems for some hypergroup
structures on R^n x [0,infinity[
Yu. M. Berezansky, Nuclear spaces of test functions connected with
hypercomplex systems and representations of such systems
Yu. M. Berezansky and A.A. Kalyuzhnyi, Hypercomplex systems and
hypergroups: Connections and distinctions
W.R. Bloom and Z. Xu, The Hardy-Littlewood maximal function for
Chebli-Trimeche hypergroups
H. Chebli, Sturm-Liouville hypergroups
W.C. Connett and A.L. Schwartz, Continuous 2-variable polynomial
hypergroups
P. Eymard, A survey of Fourier algebras
A. Fitouhi and M.M. Hamza, Expansion in series of Laguerre functions for
solution of perturbed Laguerre equations
L. Gallardo, Asymptotic behaviour of the paths of random walks on some
commutative hypergroups
M.-O. Gebuhrer, Bounded measures algebras: A fixed point approach
H. Heyer, Progress in the theory of probability on hypergroups
T.H. Koornwinder, Discrete hypergroups associated with compact quantum
Gelfand pairs
B.M. Levitan, Transmutation operators and the inverse spectral problem
M. Mabrouki, Limit theorems for the spin process
N.H. Mahmoud, Differential operators with matrix coefficients and
transmutations
B.P. Osilenker, Generalized product formulas for orthogonal polynomials
G.B. Podkolzin, An infinitesimal algebra of the hypergroup generated by
double cosets and nonlinear differential equations
M. Rosler, Convolution algebras which are not necessarily
positivity-preserving
K.A. Ross, Signed hypergroups - A survey
V.S. Sunder, On the relation between subfactors and hypergroups
R. Szwarc, Connection coefficients of orthogonal polynomials with
applications to classical orthogonal polynomials
K. Trimeche, Generalized transmutation and translation operators
associated with partial differential operators
L. Vainerman, Gel'fand pairs of quantum groups, hypergroups and
q-special functions
M. Voit, Central limit theorems for Jacobi hypergroups
N.J. Wildberger, Finite commutative hypergroups and applications from
group theory to conformal field theory
Topic #11 --------------- OP-SF NET --------------- September 7, 1995
From: Andre Ronveaux <aronveau@hermes.fundp.ac.be>
Subject: New book on Heun's differential equations
The following book will appear in October 1995:
Heun's Differential Equations
Andre Ronveaux (ed.)
with contributions by F.M. Arscott, S.Yu. Slavyanov. D. Schmidt,
G. Wolf, P. Maroni and A. Duval
Oxford University Press, October 1995, 368 pages, IBSN 859695-2
About the book:
Heun's equation is a linear second-order differential equation which
occurs in a wide range of problems in applied mathematics. This
differential equation with four regular singular points generates by
confluence four different differential equations. Areas in which these
equations occur include the integral equations of potential theory,
wave propagation, electrostatic oscillation, and Schrodinger's
equation.
A recent symposium on the topic surveyed both the current theory and
also the main areas of application. The book is a commissioned
collection of edited papers from contributors to the symposium.
Topic #12 --------------- OP-SF NET --------------- September 7, 1995
From: Walter Van Assche <Walter.VanAssche@wis.kuleuven.ac.be>
Subject: Early history of Bessel functions
Here's a reference that may be (should be) of interest to you:
Jacques Dutka: "On the early history of Bessel functions", Archive for
the History of Exact Sciences 49 (1995), No.2, 105-134.
Topic #13 --------------- OP-SF NET --------------- September 7, 1995
From: Jairo Charris <demat125@ciencias.campus.unal.edu.co>
Subject: Tenure track position in Bogota (Columbia)
The Mathematics Department at the National University of Colombia in
Bogota is trying to push forward its Ph.D. Program in Mathematics. In
order to attract competent new faculty members, it announces an
international competition for regular faculty positions. The selection
is based only on the evaluation of the curriculum vitae, on
publications, on letters of recommendation of known mathematicians and
on a proposal of the activity he plans to carry out in Colombia. It is
open to a Ph.D aged 25 to 45 with very good promise or experience in
research represented by papers published in known journals and strong
commitment of teaching at the Ph.D. level. Willingness to help
students with their dissertations is very much desirable. The
selected candidates will be granted an initial contract of one year at
the associate professor level. The salary is close to US $ 1,600 a
month (after taxes) but payment is for 15 months a year (This is
equivalent to about US $ 2,200 a month stipend in the USA). The
nature of the position is tenure track, but there is a one year
probation period and a Faculty evaluation of performance at the end of
that period. The candidate does not have to know Spanish. However,
Spanish is the official language in Colombia and it is expected the
winners of the contest will learn some Spanish during their first year
in Colombia. Some work at the Department is being done in Special
Functions, Orthogonal Polynomials, Approximation Theory and related
areas. However, Partial Differential Equations, Logic, Category
Theory, Lie Algebras and Lie Groups also belong to its priorities.
For further information please contact
Jairo Charris
Department of Mathematics
Universidad Nacional de Colombia
Santafe de Bogota
Colombia
email: demat125@ciencias.campus.unal.edu.co
Topic #14 --------------- OP-SF NET --------------- September 7, 1995
From: S. Yakubovich
Subject: Looking for a position
Dr. S. Yakubovich from Minsk (Belarus) is urgently looking for a
(regular or visiting) position or a research grant in Mathematical
Analysis and Applications. He is a specialist in the Theory of
Functions, Integral Transforms and Special Functions. He is also
experienced in programming (including computer algebra) and
implementing results on special functions. He was a coauthor of three
monographs on these topics and he published more that 60 research
papers. He is 34 years old and he has a family with two children.
More detailed information can be provided on request. Any suggestions
about possible openings are welcome. Please contact:
e-mail: semen@mmf.bsu.minsk.by
Fax: +7-0172-265 940
Mail address: P.O.Box 385
Minsk-50
220050 Belarus
(Net Editor's note: Topics like this one will only be published in
OP-SF Net in exceptional cases: in the case of unemployed researchers
with a certain reputation in the field of Orthogonal Polynomials and
Special Functions, as should be evident from the list of publications.)
Topic #15 --------------- OP-SF NET --------------- September 7, 1995
From: OP-SF Net editor <thk@fwi.uva.nl>
Subject: ftp and WWW addresses
The list of ftp and WWW addresses relevant for our field, see
OP-SF Net 2.4, Topic #22, remains available at
ftp: ftp.fwi.uva.nl
directory: pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir,
file: WWWaddresses
This file will be regularly updated, and the changes will be mentioned in
OP-SF Net.
Please mail corrections and additions for this list to me <thk@fwi.uva.nl>.
Compared to the list in OP-SF Net 2.4, there are the following changes and
additions:
MathSciNet (demo version of Math. Reviews online):
WWW: http://www.ams.org/web/mathscinet/msn-home.html
AMS preprint server:
WWW: http://e-math.ams.org/web/preprints/preprints-home.html
Centre de Recherches Mathematic, Montreal (a.o. Vinet):
WWW: http://www.crm.umontreal.ca
Topic #16 --------------- OP-SF NET --------------- September 7, 1995
From: OP-SF Net editor <thk@fwi.uva.nl>
Subject: Changes of address
The address of Willard Miller at the University of Minnesota changed to:
Willard Miller, Jr.
Professor and Acting Dean
Institute of Technology, University of Minnesota
105 Walter Library, 117 Pleasant Street S.E.
Minneapolis, Minnesota 55455
miller@ima.umn.edu 612-624-2006 FAX: 612-624-2841
Marcel de Jeu, who is working in the area of special functions associated
with root systems, will stay in Paris (Universite Paris 7, to start with)
until February 1, 1996. His address there is:
Marcel de Jeu
56 rue Oberkampf
75011 Paris
France
Tel.: +33-1 4338 7735
e-mail: dejeu@mathp7.jussieu.fr
Tom Koornwinder will stay during the period October 2 - November 23, 1995
at the Mittag Leffler Institute near Stockholm, Sweden.
Mathijs Dijkhuizen (working on special functions in connection with
quantum groups), has returned from Kobe (Japan) and will also stay
at the Mittag Leffler Institute during October and November.
The address for both will be:
Institut Mittag Leffler
Aurav\"agen 17
S-182 62 Djursholm
Sweden
tel. +46-8-755 1809
fax +46-8-755 9971
Topic #17 --------------- OP-SF NET --------------- September 7, 1995
From: OP-SF Net editor <thk@fwi.uva.nl>
Subject: Obtaining back issues of OP-SF Net
Back issues of OP-SF Net can be obtained from
ftp: ftp.fwi.uva.nl, in directory
pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir
or WWW: http://math.ohio-state.edu/JAT
Contributions to the OP-SF Net 2.6 should reach the email
address poly@siam.org before November 1, 1995.
In order to join the SIAM Activity Group on Orthogonal Polynomials
and Special Functions, and thereby receive the Newsletter,
you have to become a member of SIAM. The annual dues are $93 for
SIAM plus $10 for the Group. Contact the email address
service@siam.org.
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