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## Taylor formula for distributions

Autorzy
Seria
Rozprawy Matematyczne tom/nr w serii: 264 wydano: 1988
Zawartość
Warianty tytułu
Abstrakty
EN

CONTENTS
0. Introduction................................................................................................................................................................5
1. Preliminary remarks...................................................................................................................................................6
2. Hyperfunctions and their generalizations.................................................................................................................10
3. Flat functions; definitions and properties.................................................................................................................14
4. Taylor formula for quasi $O(x^a)$ functions.............................................................................................................18
5. Homogeneous distributions and their properties......................................................................................................20
6. Mellin transformable distributions.............................................................................................................................22
7. Differential equations in the space of Mellin transformable distributions. Operational calculus for ℳ......................26
8. Taylor formula for distributions.................................................................................................................................29
9. Taylor transformation for functions and distributions................................................................................................32
10. Spectral support of a function and of a distribution................................................................................................33
11. Determination of singularities of solutions of ordinary linear differential operators with smooth coefficients..........36
11. 1. Asymptotic expansion of the push-forward operation $F_{∗}φ$ for F admitting an F-invariant operator...........40
12. Value of a function (distribution) at a point.............................................................................................................41
13. Taylor formula for the product of functions.............................................................................................................44
14. Multiplication of distributions. Taylor formula for the product of distributions..........................................................47
14.1. Spectral topology................................................................................................................................................50
14.2. Heuristic remarks concerning multiplication of distributions.................................................................................51
14.3. Taylor formula for the function 1/f........................................................................................................................51
15. Taylor formula for composite functions...................................................................................................................52
References ..................................................................................................................................................................56
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Seria
Rozprawy Matematyczne tom/nr w serii: 264
Liczba stron
56
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCLXIV
Daty
wydano
1988
Twórcy
autor
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, Warsaw, P.O. Box 137, Poland
Bibliografia
• [1] Yu. A. Brytchkov, A. D. Prudnikov, Integral Transformations of Generalized Functions, Moscow 1977 (in Russian).
• [2] S. Colombo, Les transformations de Meilin et de Hankel.
• [3] S. Colombo, J. Lavoine, Transformations de Laplace et de Mellin, Memorial des Sciences Mathématiques, 1969.
• [4] M. Costabel, Boundary integral operators on curved polygons, Ann. Mat. Pura Appl. 133 (1983), 305-326.
• [5] J. J. Duistermaat, Fourier Integral Operators, Courant Insitute of Math. Sciences, New York 1973.
• [6] I. M. Gel'fand, G. E. Shilov, Generalized Functions, Academic Press, New York 1964.
• [7] L. Hörmander, The Analysis of Linear Partial Differential Operators, Springer-Verlag, Berlin 1983.
• [8] P. Jeanquartier, Développement asymptotique de la distribution de Dirac attachée à une fonction analytique, C.R. Acad. Sci. Paris 271 (1970), 1159-1161.
• [9] P. Jeanquartier, Transformation de Mellin et développements asymptotiques, Enseign. Math. 25 (1979), 285-308.
• [10] H. Komatsu, An introduction to the theory of hyperfunctions, Lecture Notes in Math. 287, Springer-Verlag, Berlin 1973.
• [11] S. Łojasiewicz, Sur la valeur et la limite d'une distribution dans un point, Studia Math. 16 (1957), 1-36.
• [12] J. Schmets, Hyperfonctions et microfonctions d'une variable, Institut de Mathématique, Université de Liège, preprint.
• [13] J. H. Sneddon, The Use of Integral Transforms, New York 1972.
• [14] Z. Szmydt. B. Ziemian, Explicit invariant solutions for invariant linear differential operators, Proc. Royal Soc. Edinburgh 98 (1984), 149-166.
• [15] A. Weinstein, The order and the symbol of a distribution, Trans. Amer. Math. Soc. 241 (1978), 1-54.
• [16] D. V. Widder, The Laplace transform, Princeton Univ. Press, Princeton, NJ., 1946.
• [17] A. H. Zemanian, Generalized integral transformations, Interscience Publishers, 1969.
• [18] B. Ziemian, A Taylor type decomposition for distributions in one dimension, Bull. Polish Acad. Sci. 32 (1984), 143-155.
• [19] B. Ziemian, An analysis of microlocal singularities of functions and distributions on the real line, ibidem, 156-164.
• [20] B. Ziemian, The derivative of a measurable function and of a distribution at a point and its basic properties, ibidem, 165-177.
Języki publikacji
 EN
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