## Generalized Functions, Convergence Structures, and Their ApplicationsThis 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

4 | |

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 |

### Other editions - View all

Generalized Functions, Convergence Structures, and Their Applications Bogoljub Stankovic No preview available - 2011 |

Generalized Functions, Convergence Structures, and Their Applications Bogoljub Stankovic No preview available - 1988 |

### Common terms and phrases

algebra arbitrary assume boundary value bounded Cauchy space Cauchy vector space Colombeau compact support complete continuous function convergence Corollary countable defined Definition denote differential equations elements equivalent example exists filter monad finite Fock space formula Fourier transform Fréchet Fréchet space func function F functor Hence holomorphic function hyperfunctions implies inductive limit isomorphism Laplace transform Lemma Let f linear locally convex Math matrix Mikusiński monad morphism norm Novi Sad obtain operational calculus Pilipović polynomial problem Proof Proposition prove regular convolution quotient representation resp respect result Riesz space S-asymptotic satisfies Schwartz sequence sheaf solution Stieltjes transformation subset subspace tempered distributions test functions Theorem theory tions topology weakly zero