A Phragmén-Lindelöf type quasi-analyticity principle

Grzegorz Łysik

Studia Mathematica (1997)

  • Volume: 123, Issue: 3, page 217-234
  • ISSN: 0039-3223

Abstract

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Quasi-analyticity theorems of Phragmén-Lindelöf type for holomorphic functions of exponential type on a half plane are stated and proved. Spaces of Laplace distributions (ultradistributions) on ℝ are studied and their boundary value representation is given. A generalization of the Painlevé theorem is proved.

How to cite

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Łysik, Grzegorz. "A Phragmén-Lindelöf type quasi-analyticity principle." Studia Mathematica 123.3 (1997): 217-234. <http://eudml.org/doc/216390>.

@article{Łysik1997,
abstract = {Quasi-analyticity theorems of Phragmén-Lindelöf type for holomorphic functions of exponential type on a half plane are stated and proved. Spaces of Laplace distributions (ultradistributions) on ℝ are studied and their boundary value representation is given. A generalization of the Painlevé theorem is proved.},
author = {Łysik, Grzegorz},
journal = {Studia Mathematica},
keywords = {quasi-analyticity; Laplace distributions; Laplace ultradistributions; boundary values},
language = {eng},
number = {3},
pages = {217-234},
title = {A Phragmén-Lindelöf type quasi-analyticity principle},
url = {http://eudml.org/doc/216390},
volume = {123},
year = {1997},
}

TY - JOUR
AU - Łysik, Grzegorz
TI - A Phragmén-Lindelöf type quasi-analyticity principle
JO - Studia Mathematica
PY - 1997
VL - 123
IS - 3
SP - 217
EP - 234
AB - Quasi-analyticity theorems of Phragmén-Lindelöf type for holomorphic functions of exponential type on a half plane are stated and proved. Spaces of Laplace distributions (ultradistributions) on ℝ are studied and their boundary value representation is given. A generalization of the Painlevé theorem is proved.
LA - eng
KW - quasi-analyticity; Laplace distributions; Laplace ultradistributions; boundary values
UR - http://eudml.org/doc/216390
ER -

References

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  1. [H] E. Hille, Analytic Function Theory, Vol. 2, Chelsea, New York, 1962. Zbl0102.29401
  2. [K] H. Komatsu, Ultradistributions, I. Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo 20 (1973), 25-105. Zbl0258.46039
  3. [Ł1] G. Łysik, Generalized analytic functions and a strong quasi-analyticity principle, Dissertationes Math. 340 (1995), 195-200. Zbl0882.46018
  4. [Ł2] G. Łysik, Laplace ultradistributions on a half line and a strong quasi-analyticity principle, Ann. Polon. Math. 63 (1996), 13-33. Zbl0843.46025
  5. [M] S. Mandelbrojt, Séries adhérentes, régularisation des suites, applications, Gauthier-Villars, Paris, 1952. Zbl0048.05203
  6. [R] C. Roumieu, Sur quelques extensions de la notion de distribution, Ann. Sci. École Norm. Sup. 77 (1960), 41-121. Zbl0104.33403
  7. [SZ] Z. Szmydt and B. Ziemian, The Laplace distributions on ℝ + n , submitted to J. Math. Sci. Univ. Tokyo. 
  8. [T] J. C. Tougeron, Gevrey expansions and applications, preprint, University of Toronto, 1991. 
  9. [W] D. V. Widder, The Laplace Transform, Princeton Univ. Press, Princeton, N.J., 1946. Zbl0060.24801
  10. [Z] A. H. Zemanian, Generalized Integral Transformations, Interscience, 1969. Zbl0181.12701

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