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The asymptotic analysis has obtained new impulses with the general
development of various branches of mathematical analysis and their
applications. In this book, such impulses originate from the use of
slowly varying functions and the asymptotic behavior of generalized
functions. The most developed approaches related to generalized
functions are those of Vladimirov, Drozhinov and Zavyalov, and that
of Kanwal and Estrada. The first approach is followed by the
authors of this book and extended in the direction of the
S-asymptotics. The second approach - of Estrada, Kanwal and Vindas
- is related to moment asymptotic expansions of generalized
functions and the Ces'aro behavior. The main features of this book
are the uses of strong methods of functional analysis and
applications to the analysis of asymptotic behavior of solutions to
partial differential equations, Abelian and Tauberian type theorems
for integral transforms as well as for the summability of Fourier
series and integrals. The book can be used by applied
mathematicians, physicists, engineers and others who use classical
asymptotic methods and wish to consider non-classical objects
(generalized functions) and their asymptotics now in a more
advanced setting.
This Proceedings consists of a collection of papers presented at
the International Conference "Generalized functions, convergence
structures and their applications" held from June 23-27, 1987 in
Dubrovnik, Yugoslavia (GFCA-87): 71 participants from 21 countr es
from allover the world took part in the Conference. Proceedings
reflects the work of the Conference. Plenary lectures of J. Burzyk,
J. F. Colombeau, W. Gahler, H. Keiter, H. Komatsu, B. Stankovic, H.
G. Tillman, V. S. Vladimirov provide an up-to-date account of the
cur rent state of the subject. All these lectures, except H. G.
Tillman's, are published in this volume. The published
communications give the contemporary problems and achievements in
the theory of generalized functions, in the theory of convergence
structures and in their applications, specially in the theory of
partial differential equations and in the mathematical physics. New
approaches to the theory of generalized functions are presented,
moti vated by concrete problems of applications. The presence of
articles of experts in mathematical physics contributed to this
aim. At the end of the volume one can find presented open problems
which also point to further course of development in the theory of
generalized functions and convergence structures. We are very
grateful to Mr. Milan Manojlovic who typed these Proce edings with
extreme skill and diligence and with inexhaustible patience."
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