Generalized Functions, Convergence Structures, and Their Applications

1. Front Matter

   Pages i-xi

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2. Plenary Lectures

   1. Front Matter

      Pages 1-1

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   2. Nonharmonic Solutions of the Laplace Equation

      • Jozef Burzyk

      Pages 3-11

   3. Generalized Functions; Multiplication of Distributions; Applications to Elasticity, Elastoplasticity, Fluid Dynamics and Acoustics

      • J. F. Colombeau

      Pages 13-27

   4. Monads and Convergence

      • Werner Gähler

      Pages 29-46

   5. Simple Applications of Generalized Functions in Theoretical Physics: The Case of Many–Body Perturbation Expansions

      • H. F. G. Keiter

      Pages 47-55

   6. Laplace Transforms of Hyperfunctions: Another Foundation of the Heaviside Operational Calculus

      • Hikosaburo Komatsu

      Pages 57-70

   7. S-Asymptotic of Distributions

      • Bogoljub Stanković

      Pages 71-82

   8. The Wiener-Hopf Equation in the Nevanlinna and Smirnov Algebras and Ultra-Distributions

      • V. S. Vladimirov

      Pages 83-96

3. Generalized Functions

   1. Front Matter

      Pages 97-97

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   2. On Nonlinear Systems of Ordinary Differential Equations

      • Lothar Berg

      Pages 99-111

   3. A New Construction of Continuous Endomorphisms of the Operator Field

      • A. Bleyer

      Pages 113-119

   4. Some Comments on the Burzyk-Paley-Wiener Theorem for Regular Operators

      • Thomas K. Boehme

      Pages 121-124

   5. Two Theorems on the Differentiation of Regular Convolution Quotients

      • Thomas K. Boehme

      Pages 125-129

   6. Values on the Topological Boundary of Tubes

      • Richard D. Carmichael

      Pages 131-138

   7. Abelian Theorem for the Distributional Stieltjes Transformation

      • Danica Nikolić-Despotović, Stevan Pilipović

      Pages 139-146

   8. Some Results on the Neutrix Convolution Product of Distributions

      • Brian Fisher

      Pages 147-155

   9. On Generalized Transcedental Functions and Distributional Transforms

      • A. N. Goyal, V. K. Chaturvedi

      Pages 157-170

   10. An Algebraic Approach to Distribution Theories

       • J. de Graaf, A. F. M. ter Elst

       Pages 171-177

   11. Products of Wiener Functionals on an Abstract Wiener Space

       • Shiro Ishikawa

       Pages 179-185

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.

• Derivative
• algebra
• calculus
• differential equation
• non-standard analysis

• Institute of Mathematics, Novi Sad, Yugoslavia

  Bogoljub Stanković, Endre Pap, Stevan Pilipović

• Steklov Institute of Mathematics, Moscow, USSR

  Vasilij S. Vladimirov

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