Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Cover of the book
Tytuł książki

Topological imbedding of Laplace distributions in Laplace hyperfunctions

Seria
Rozprawy Matematyczne tom/nr w serii: 376 wydano: 1998
Zawartość
Warianty tytułu
Abstrakty
EN
CONTENTS
Foreword..............................................................................................................................5
Introduction..........................................................................................................................6
1. Preliminaries....................................................................................................................7
 1.1. Terminology and notation.............................................................................................7
 1.2. Selected topics on complex topological vector spaces and their duals........................7
2. A review of basic facts in the theory of distributions.......................................................10
 2.1. The spaces $D_K$ and $(D_K)'$..............................................................................10
 2.2. The spaces D(Ω) and D'(Ω).......................................................................................11
 2.3. The spaces D(A) and D'(A)........................................................................................12
 2.4. The spaces $D^k(K)$ and $(D^k(K))'$.......................................................................14
3. Selected topics in the theory of holomorphic functions of one variable..........................15
 3.1. Basic notions and theorems.......................................................................................15
 3.2. The spaces A(K) and A'(K)........................................................................................16
 3.3. Boundary values of holomorphic functions of one variable........................................19
4. Hyperfunctions in one variable.......................................................................................23
 4.1. Definitions and basic properties of hyperfunctions....................................................23
 4.2. Imbedding of analytic functions in hyperfunctions: A(Ω) ↪ B(Ω)................................26
 4.3. Elementary operations on hyperfunctions..................................................................27
 4.4. The Köthe theorem....................................................................................................28
 4.5. Imbedding $D'_K ↪ B_K$, K compact in ℝ................................................................31
 4.6. The distributional version of the Köthe theorem........................................................34
 4.7. Imbedding D'(Ω)↪ B(Ω), Ω open in ℝ........................................................................35
 4.8. Hyperfunctional boundary values of holomorphic functions.......................................39
 4.9. Hyperfunctions supported by a single point...............................................................39
 4.10. Substitution in a hyperfunction and in an analytic functional (distribution)...............40
5. Laplace hyperfunctions and Laplace analytic functionals in one variable......................42
6. Mellin hyperfunctions and Mellin distributions in one variable........................................50
 6.1. Mellin hyperfunctions and Mellin analytic functionals.................................................50
 6.2. Mellin distributions.....................................................................................................60
7. Laplace distributions L'(ω)(ℝ͞͞₊)......................................................................................64
 7.1. Definitions and basic properties of Laplace distributions...........................................64
 7.2. Imbedding of Laplace distributions in Laplace hyperfunctions...................................67
 7.3. Imbedding of Mellin distributions in Mellin hyperfunctions..........................................79
References........................................................................................................................81
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 376
Liczba stron
81
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLXXVI
Daty
wydano
1998
otrzymano
1997-11-03
poprawiono
1998-03-18
Twórcy
autor
  • Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 137, 00-950 Warszawa, Poland
  • Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 137, 00-950 Warszawa, Poland
Bibliografia
  • [B] H. Bremermann, Distributions, Complex Variables and Fourier Transform, Addison-Wesley, Reading, 1965.
  • [H] J. Horvath, Topological Vector Spaces and Distributions I, Addison-Wesley, Reading, 1966.
  • [Hö1] L. Hörmander, An Introduction to Complex Analysis in Several Variables, D. Van Nostrand, Princeton, 1967.
  • [Hö2] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, Berlin, 1985.
  • [K] A. Kaneko, Introduction to Hyperfunctions, Math. Appl., Kluwer, Dordrecht, 1988.
  • [Ko1] H. Komatsu, Relative cohomology of sheaves of solutions of differential equations, in: Hyperfunctions and Pseudo-Differential Equations, Lecture Notes in Math. 287, Springer, Berlin, 1973, 192-261.
  • [Ko2] H. Komatsu, Ultradistributions I, J. Fac. Sci. Univ. Tokyo Sect. IA 20 (1973), 25-105.
  • [Kö] G. Köthe, Dualität in der Funktionentheorie, J. Reine Angew. Math. 191 (1953), 30-49.
  • [M-Y] M. Morimoto and K. Yoshino, Some examples of analytic functionals with carrier at infinity, Proc. Japan Acad. Ser. A Math. Sci. 56 (1980), 357-361.
  • [N] R. Narasimhan, Several Complex Variables, Chicago Lectures in Math., Univ. Chicago Press, Chicago, 1971.
  • [P-Z] M. E. Pliś and B. Ziemian, Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables, Ann. Polon. Math. 67 (1997), 31-41.
  • [R] W. Rudin, Lectures on the Edge-of-the-Wedge Theorem, CBMS Regional Conf. Ser. in Math. 6, Amer. Math. Soc., Providence, 1971.
  • [S] R. T. Seeley, Extension of $C^∞$ functions defined in a half space, Proc. Amer. Math. Soc. 15 (1964), 625-626.
  • [St] E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1970.
  • [Sz] Z. Szmydt, Fourier Transformation and Linear Differential Equations, PWN-Polish Sci. Publ., Warszawa, and D. Reidel, Dordrecht, 1977.
  • [Sz-Z1] Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type Partial Differential Equations, Math. Appl., Kluwer, Dordrecht, 1992.
  • [Sz-Z2] Z. Szmydt and B. Ziemian, Laplace distributions and hyperfunctions on ℝ͞͞₊ⁿ, J. Math. Sci. Univ. Tokyo 5 (1998), 41-74.
  • [W] A. Wawrzyńczyk, Group Representations and Special Functions, D. Reidel, Dordrecht, and PWN-Polish Sci. Publ., Warszawa, 1984.
  • [Z1] B. Ziemian, Generalized analytic functions with application to singular ordinary and partial differential equations, Dissertationes Math. 354 (1996).
  • [Z2] B. Ziemian, Leray residue formula and asymptotics of solutions to constant coefficient PDEs, Topol. Methods Nonlinear Anal. 3 (1994), 257-293.
  • [Z3] B. Ziemian, Holomorphic regularizations of meromorphic functions, to appear.
Języki publikacji
EN
Uwagi
1991 Mathematics Subject Classification: 46F12, 46F15, 46F20.
Identyfikator YADDA
bwmeta1.element.zamlynska-0012a239-5764-4678-9bfb-5ab892a8ac3b
Identyfikatory
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki

rozwiń roczniki

JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.