SIAM AG on Orthogonal Polynomials and Special Functions


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The following report appeared in our October 1996 printed Newsletter.

From: Rudolf Gorenflo 
Subject: Second International Workshop Transform Methods & Special
       Functions: Varna, Bulgaria, August 23-30, 1996

This workshop, whose scientific program lasted from August
24 to August 29, 1996, was organized by:

  1. Institute of Mathematics and Informatics of the Bulgarian Academy of
       Sciences; 

  2. Institute of Applied Mathematics and Computer Sciences of Technical
       University Sofia;

  3. Union of Bulgarian Mathematicians;

  4. Union of Scientists in Bulgaria;

  5. Istituto per la Ricerca di Base (Monteroduni, Italy).

It took place in the hotels Magnolia and Detelina, north of Varna, with a
wide view of the Black Sea. It was dedicated to the 100th anniversary of
the birth of the Bulgarian mathematician Academician Nikola Obrechkoff
(1896-1963, born in Varna) who did pioneering work in such diverse fields
as analysis, algebra, number theory, numerical analysis, summation of
divergent series, probability and statistics.  The workshop was attended
by more than seventy participants from twenty countries, alphabetically
from Australia to Vietnam, the largest groups coming from Poland (20),
Bulgaria (12) and Japan (7). 

After the opening ceremonies (which included a greeting speech from
Varna's Mayor and an appreciation of Obrechkoff and his achievements by
I. Dimovski (Sofia) the series of lectures commenced with a plenary
lecture by Prof. E.R. Love from Melbourne (Australia), the oldest
participant at the Conference, on his joint work with M.N. Hunter on
"Expansions in series of Legendre functions". 

In total there were six plenary lectures, presented by E.R. Love (title
already mentioned), F. Mainardi (Bologna, Italy) on "Applications of
fractional calculus in mechanics", R. Gorenflo (Berlin, Germany) on "The
tomato salad problem in spherical stereology, P.G. Rooney (Toronto,
Canada) on "The ranges of Mellin multiplier transformations",
H.M. Srivastava (Victoria, Canada) on "Some operational techniques in the
theory of special functions", and Vu Kim Tuan (Kuwait) on "Integral
transforms and supports of functions." Then 63 lectures were presented in
(up to three)  parallel sessions with headings "Integral Transforms and
Special Functions", "Fractional Calculus", "Special Functions",
"Geometric Theory of Functions", "Differential Equations", "Integral
Transforms & Operational Calculi", "Mathematical Analysis and
Applications", "Integral Transforms", "Varia". In addition, in the
closing session P. Rusev, I. Dimovski and V. Kiryakova lectured on
"Obrechkoff's generalization of Descartes' rule" and "Obrechkoff's
integral transforms". 

The conference ended with a final ceremony in which P. Antosik (Katowice,
Poland) distributed prizes (to the three largest delegations) and praise
(to individuals). 

In the lectures, besides some educational reviews, many new research
results were presented. This reporter, due to the multiple sessions, could
not attend all the talks; however he feels it appropriate to mention three
of them he considered special highlights in that they gave impressive
recent results, obtained just in the few weeks preceding the conference.
They were two lectures by P.L. Butzer and S. Jansche (Aachen, Germany) on
"The Mellin transform, finite Mellin transform and Mellin-Fourier
transform", "The Mellin-Poisson summation formula and the exponential
sampling theorem", and the plenary lecture by Vu Kim Tuan. In many
lectures the importance of special and of general types of special
functions for applications inside and outside of mathematics was stressed.
Particular mention should be made of hypergeometric functions and their
generalizations, $H$ and $G$ functions, confluent hypergeometric
functions, Bessel functions, Mittag-Leffler functions, and various types
of orthogonal polynomials. 

The program also provided a two-hour plenary discussion on "Physical and
geometrical meanings and applications of fractional calculus operators"
that was well attended and opened stimulating aspects. Topics of
discussion were, among other things, some problems raised in
H.M. Srivastava's collection of "Open questions for further researches on
fractional calculus and its applications" (pp. 281-284 in K. Nishimoto,
ed., Fractional Calculus and its Applications, Nihon University, Tokyo
1990). In particular, arguments were exchanged on the question whether
there is a relationship between fractional calculus and fractal geometry
or whether the only relationship is the coincidence of the first five
characters of the words "fractional" and "fractal".  Fortunately, the
discussion did not stick to this problem. 

The meeting was framed, thanks to the organizers P. Rusev, I. Dimovski,
V. Kiryakova, L. Boyadjiev (all from Sofia) and Sh. Kalla (Kuwait), by an
appealing social program (reception, on August 27 a whole-day excursion to
the old town Shumen, 100 km to the west of Varna, birth-place of
Prof. Rusev, and the fascinating surroundings of Shumen, with more than
two hours of Bulgarian folklore and after-lunch dancing, and on August 28
a celebration of Prof.  Rusev's 65th birthday). 

Thanks to St. Peter Black Sea sunrises, beach, sand, sun and clear water
swimming could be enjoyed. The organizing committee did, in an admirable
manner, their best to smooth all the (in retrospect, few)  problems that
are bound to arise in such a meeting. 

The Workshop's Proceedings (like those of the preceding one held in
Bankya/Bulgaria, 12-17 August 1994) will be published by "Science Culture
Technology (SCT) Publishing" in Singapore. 

Rudolf Gorenflo 




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