Generalized Functions, Convergence Structures, and Their Applications

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Bogoljub Stankovic
Springer Science & Business Media, Dec 6, 2012 - Mathematics - 464 pages
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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Contents

Nonharmonic solutions of the Laplace equation
4
Generalized functions multiplication of distributions applications
13
Monads and convergence
29
another foundation of
57
Sasymptotic of distributions
71
The WienerHopf equation in the Nevanlinna and Smirnov algebras
82
On nonlinear systems of ordinary differential equations
98
A new construction of continuous endomorphisms of the operator field
113
Some important results of distribution theory
251
Estimations for the solutions of operator linear differential
267
Invariance of the Cauchy problem for distribution differential
279
Mn On the space 0 P q 1
285
Peetres theorem and generalized functions
297
Infinite dimensional Fock spaces and an associated generalized
305
The ndimensional Stieltjes transformation
317
Colombeaus generalized functions and nonstandard analysis
327

Some comments on the BurzykPaleyWiener theorem for regular
121
Values on the topological boundary of tubes
131
Abelian theorem for the distributional Stieltjes transformation
139
Some results on the neutrix convolution product of distributions
147
On generalized transcedental functions and distributional
157
An algebraic approach to distribution theories
171
Products of Wiener functionals on an abstract Wiener space
179
Convolution in K Mpspaces
187
The problem of the jump and the Sokhotski formulas in the space
197
A generalized fractional calculus and integral transforms
205
On the generalized Meijer transformation
219
The construction of regular spaces and hyperspaces with respect
227
Operational calculus with derivative sº
235
Solvability of nonlinear operator equations with applications
245
One product of distributions
341
Abel summability for a distribution sampling theorem
349
On the value of a distribution at a point
359
On interchange of 1jmits
367
Countability completeness and the closed graph theorem
375
Inductive limits of Riesz spaces
383
Convergence completion of partially ordered groups
393
Some results from nonlinear analysis in limit vector spaces
399
Completions of Cauchy vector spaces
409
Regular inductive limits
415
The BanachSteinhaus theorem for ordered spaces 425
424
OPEN PROBLEMS
435
Participants
443
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