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1992 | 102 | 1 | 1-24
Tytuł artykułu

The modified Cauchy transformation with applications to generalized Taylor expansions

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We generalize to the case of several variables the classical theorems on the holomorphic extension of the Cauchy transforms. The Cauchy transformation is considered in the setting of tempered distributions and the Cauchy kernel is modified to a rapidly decreasing function. The results are applied to the study of "continuous" Taylor expansions and to singular partial differential equations.
Słowa kluczowe
Czasopismo
Rocznik
Tom
102
Numer
1
Strony
1-24
Opis fizyczny
Daty
wydano
1992
otrzymano
1990-10-12
poprawiono
1991-04-16
Twórcy
  • Institute of Mathematics, Polish Academy of Sciences, P.o. Box 137, 00-950 Warszawa, Poland
Bibliografia
  • [1] H. Bremermann, Distributions, Complex Variables and Fourier Transform, Addison-Wesley, 1965.
  • [2] A. Kaneko, Introduction to Hyperfunctions, Math. Appl., Kluwer, Dordrecht 1988.
  • [3] H. Komatsu, An introduction to the theory of hyperfunctions, in: Lecture Notes in Math. 287, Springer, 1973, 1-43.
  • [4] H. M. Reimann, Transformation de Fourier et intégrales singulières, Cours d'analyse harmonique 1982/83, Université de Berne.
  • [5] W. Rudin, Lectures on the Edge-of-the-Wedge Theorem, CBMS Regional Conf. Ser. in Math. 6, Amer. Math. Soc., 1971.
  • [6] J. Schmets, Hyperfonctions et microfonctions d'une variable, Publications d'Institut de Mathématique, Université de Liège, 1979-1980.
  • [7] Z. Szmydt, The Paley-Wiener theorem for the Mellin transformation, Ann. Polon. Math. 51 (1990), 313-324.
  • [8] Z. Szmydt and B. Ziemian, Multidimensional Mellin transformation and partial differential operators with regular singularities, Bull. Polish Acad. Sci. Math. 35 (1987), 167-180.
  • [9] Z. Szmydt and B. Ziemian, Solutions of singular elliptic equations via the Mellin transformation on sets of high order of tangency to the singular lines, ibid. 36 (1988), 521-535.
  • [10] Z. Szmydt and B. Ziemian, Local existence and regularity of solutions of singular elliptic operators on manifolds with corner singularities, J. Differential Equations 23 (1990), 1-25.
  • [11] Z. Szmydt and B. Ziemian, Characterization of Mellin distributions supported by certain noncompact sets, this issue, 25-38.
  • [12] Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type Partial Differential Equations, book to be published by Kluwer Academic Publishers.
  • [13] B. Ziemian, An analysis of microlocal singularities of functions and distributions on the real line, Bull. Polish Acad. Sci. Math. 32 (1984), 157-164.
  • [14] B. Ziemian, Taylor formula for distributions in several dimensions, ibid. 34 (1986), 277-286.
  • [15] B. Ziemian, Taylor formula for distributions, Dissertationes Math. 264 (1988).
  • [16] B. Ziemian, The Mellin transformation and multidimensional generalized Taylor expansions of singular functions, J. Fac. Sci. Univ. Tokyo 36 (1989), 263-295.
  • [17] B. Ziemian, Elliptic corner operators in spaces with continuous radial asymptotics I, J. Differential Equations, to appear.
  • [18] B. Ziemian, Elliptic corner operators in spaces with continuous radial asymptotics II, in: Banach Center Publ. 27, to appear.
  • [19] B. Ziemian, Continuous radial asymptotic for solutions to elliptic Fuchsian equations in 2 dimensions, in: Proc. Sympos. Microlocal Analysis and its Applications, RIMS Kokyuroku 750, Kyoto Univ., 1991, 3-19.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv102i1p1bwm
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