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Warianty tytułu
Abstrakty
CONTENTS
Introduction........................................................................................................... 3
§ 1. The abstraction principle............................................................................... 4
§ 2. Fundamental sequences of continuous functions......................................... 5
§ 3. The definition of distributions........................................................................ 9
§ 4. Distributions as a generalization of the notion of functions........................... 11
§ 5. Algebraic operations on distributions............................................................ 12
§ 6. Derivation of distributions.............................................................................. 13
§ 7. The definition of distributions by derivatives................................................. 16
§ 8. Locally integrable functions........................................................................... 17
§ 9. Sequences and series of distributions.......................................................... 19
§ 10. Distributions depending on a continuous parameter................................... 23
§ 11. Multiplication of distributions by functions.................................................... 25
§ 12. Substitutions................................................................................................ 27
§ 13. Equality of distributions in intervals............................................................. 30
§ 14. Functions with poles.................................................................................... 32
§ 15. Derivative as the limit of a difference quotient............................................. 33
§ 16. The value of a distribution at a point............................................................ 35
§ 17. Existence theorems for values of distributions............................................. 37
§ 18. The value of a distribution at infinity............................................................. 41
§ 19. The integral of a distribution......................................................................... 42
§ 20. Periodic distributions.................................................................................... 46
§ 21. Distributions of infinite order......................................................................... 51
References............................................................................................................ 54
Introduction........................................................................................................... 3
§ 1. The abstraction principle............................................................................... 4
§ 2. Fundamental sequences of continuous functions......................................... 5
§ 3. The definition of distributions........................................................................ 9
§ 4. Distributions as a generalization of the notion of functions........................... 11
§ 5. Algebraic operations on distributions............................................................ 12
§ 6. Derivation of distributions.............................................................................. 13
§ 7. The definition of distributions by derivatives................................................. 16
§ 8. Locally integrable functions........................................................................... 17
§ 9. Sequences and series of distributions.......................................................... 19
§ 10. Distributions depending on a continuous parameter................................... 23
§ 11. Multiplication of distributions by functions.................................................... 25
§ 12. Substitutions................................................................................................ 27
§ 13. Equality of distributions in intervals............................................................. 30
§ 14. Functions with poles.................................................................................... 32
§ 15. Derivative as the limit of a difference quotient............................................. 33
§ 16. The value of a distribution at a point............................................................ 35
§ 17. Existence theorems for values of distributions............................................. 37
§ 18. The value of a distribution at infinity............................................................. 41
§ 19. The integral of a distribution......................................................................... 42
§ 20. Periodic distributions.................................................................................... 46
§ 21. Distributions of infinite order......................................................................... 51
References............................................................................................................ 54
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
12
Liczba stron
54
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom XII
Daty
wydano
1957
Twórcy
autor
autor
Bibliografia
- [1] I. Halperin, Introduction to the theory of distributions, Toronto 1952.
- [2] H. König, Neue Begründung der Theorie der ,,Distributionen” von. Schwartz, Mathematische Nachrichten 9 (1953), p. 130-148.
- [3] J. Korevaar, Distributions defined from the point of view of applied mathematics, Proceedings Kon. Nederl. Akad. Wetenschappen Series A, No 2 and Indag. Math. 17.2 (1955), p. 368-383; ibidem Series A, 58.4 and 17.4 (1955), p. 463-503; ibidem Series A, 58.5 and 17.5 (1955), p. 563-674.
- [4] S. Łojasiewicz, Sur la valeur d’une distribution dans un point, Bull. Pol. Acad. Sc. Cl. Ill, 4 (1956), p. 239-242.
- [5] S. Łojasiewicz Sur la valeur et la limite l’une distribution dans un point, Studia Math. 16 (1957), p. 1-36.
- [6] S. Łojasiewicz, J. Wloka und Z. Zielezny, Über eine Définition des Wertes einer Distribution, Bull. Acad. Pol. Sc. Cl. III, 3 (1955), p. 479-481.
- [7] J. Mikusiński, Sur la méthode de généralisation de M. Laurent Schwartz et sur la convergence faible, Fund. Math. 35 (1948), p. 235-239.
- [8] J. Mikusiński, Une définition de distribution, Bull. Acad. Pol. Sc. Cl. III, 3 (1955), p. 589-591.
- [9] L. Schwartz, Généralisation de la notion de fonction, de dérivation, de transformation de Fourier, et applications mathématiques et physiques, Annales Univ. Grenoble 21 (1945), p. 57-74.
- [10] L. Schwartz, Théorie des distributions I, Paris 1950.
- [11] L. Schwartz, Théorie des distributions II, Paris 1951.
- [12] R. Sikorski, A definition of the notion of distribution, Bull. Acad. Pol. Sc. Cl. III, 2 (1954), p. 209-211.
- [13] W. Słowikowski, A generalization of the theory of distributions, Bull. Acad. Pol. Sc. Cl. III, 3 (1955), p. 3-6.
- [14] W. Słowikowski, On the theory of operator systems, Bull. Acad. Pol. Sc. Cl. III, 3 (1955), p. 137-142.
- [15] S. Soboleff, Méthode nouvelle à résoudre le problème de Cauchy pour les équations hyperboliques normales, Recueil Math. (Mat. Sbornik) 1 (1936), p. 39-71.
- [16] G. Temple, Theories and applications of generalized functions, Journal of the London Math. Soc. 28 (1953), p. 134-148.
- [17] J. Wloka, Über die Gleichwertigkeit zweier Stetigkeitsdefinitionen, (in print).
- [18] Z. Zieleźny, Sur la définition de Łojasiewicz de la valeur d’une distribution dans Un point, Bull. Acad. Pol. Sc. Cl. III, 3 (1955), p. 519-520.
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