The following report appeared in our October 1996 printed Newsletter. From: Rudolf GorenfloSubject: 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

Back to Home Page of

SIAM AG on Orthogonal Polynomials and Special Functions

Page maintained by Martin Muldoon