Laplace ultradistributions on a half line and a strong quasi-analyticity principle

Grzegorz Łysik

Annales Polonici Mathematici (1996)

  • Volume: 63, Issue: 1, page 13-33
  • ISSN: 0066-2216

Abstract

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Several representations of the space of Laplace ultradistributions supported by a half line are given. A strong version of the quasi-analyticity principle of Phragmén-Lindelöf type is derived.

How to cite

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Grzegorz Łysik. "Laplace ultradistributions on a half line and a strong quasi-analyticity principle." Annales Polonici Mathematici 63.1 (1996): 13-33. <http://eudml.org/doc/262642>.

@article{GrzegorzŁysik1996,
abstract = {Several representations of the space of Laplace ultradistributions supported by a half line are given. A strong version of the quasi-analyticity principle of Phragmén-Lindelöf type is derived.},
author = {Grzegorz Łysik},
journal = {Annales Polonici Mathematici},
keywords = {ultradistributions; boundary values; quasi-analyticity; representations; space of Laplace ultradistributions supported by a half line; quasi-analyticity principle of Phragmén-Lindelöf type},
language = {eng},
number = {1},
pages = {13-33},
title = {Laplace ultradistributions on a half line and a strong quasi-analyticity principle},
url = {http://eudml.org/doc/262642},
volume = {63},
year = {1996},
}

TY - JOUR
AU - Grzegorz Łysik
TI - Laplace ultradistributions on a half line and a strong quasi-analyticity principle
JO - Annales Polonici Mathematici
PY - 1996
VL - 63
IS - 1
SP - 13
EP - 33
AB - Several representations of the space of Laplace ultradistributions supported by a half line are given. A strong version of the quasi-analyticity principle of Phragmén-Lindelöf type is derived.
LA - eng
KW - ultradistributions; boundary values; quasi-analyticity; representations; space of Laplace ultradistributions supported by a half line; quasi-analyticity principle of Phragmén-Lindelöf type
UR - http://eudml.org/doc/262642
ER -

References

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  1. [1] E. Hille, Analytic Function Theory, Vol. 2, Chelsea, New York, 1962. Zbl0102.29401
  2. [2] H. Komatsu, Ultradistributions, I. Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo 20 (1973), 25-105. Zbl0258.46039
  3. [3] H. Komatsu, Ultradistributions, II. The kernel theorem and ultradistributions with support in a submanifold, J. Fac. Sci. Univ. Tokyo 24 (1977), 607-628. Zbl0385.46027
  4. [4] M. Langenbruch, Bases in spaces of ultradifferentiable functions with compact support, Math. Ann. 281 (1988), 31-42. Zbl0627.46047
  5. [5] G. Łysik, Generalized analytic functions and a strong quasi-analyticity principle, Dissertationes Math. 340 (1995), 195-200. Zbl0882.46018
  6. [6] S. Mandelbrojt, Séries adhérentes, régularisation de suites, applications, Gauthier-Villars, Paris, 1952. Zbl0048.05203
  7. [7] R. Meise and A. Taylor, Linear extension operators for ultradifferentiable functions of Beurling type on compact sets, Amer. J. Math. 111 (1989), 309-337. Zbl0696.46001
  8. [8] M. Morimoto, Analytic functionals with non-compact carrier, Tokyo J. Math. 1 (1978), 77-103. Zbl0384.46027
  9. [9] S. Pilipović, Tempered ultradistributions, Boll. Un. Mat. Ital. B (7) 2 (1988), 235-251. Zbl0657.46030
  10. [10] C. Roumieu, Ultra-distributions définies sur ℝ n et sur certaines classes de variétés différentiables, J. Anal. Math. 10 (1962-63), 153-192. Zbl0122.34802
  11. [11] Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type Partial Differential Equations, Kluwer, Dordrecht, 1992. Zbl0771.35002
  12. [12] A. H. Zemanian, Generalized Integral Transformations, Interscience, 1969. 
  13. [13] B. Ziemian, Generalized analytic functions, Dissertationes Math., to appear. 

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