A Phragmén-Lindelöf type quasi-analyticity principle
Łysik, Grzegorz
Studia Mathematica, Tome 122 (1997), p. 217-234 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:216390 
@article{bwmeta1.element.bwnjournal-article-smv123i3p217bwm,
     author = {Grzegorz \L ysik},
     title = {A Phragm\'en-Lindel\"of type quasi-analyticity principle},
     journal = {Studia Mathematica},
     volume = {122},
     year = {1997},
     pages = {217-234},
     zbl = {0895.30020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv123i3p217bwm}
}

Łysik, Grzegorz. A Phragmén-Lindelöf type quasi-analyticity principle. Studia Mathematica, Tome 122 (1997) pp. 217-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv123i3p217bwm/

[00000] [H] E. Hille, Analytic Function Theory, Vol. 2, Chelsea, New York, 1962. | Zbl 0102.29401

[00001] [K] H. Komatsu, Ultradistributions, I. Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo 20 (1973), 25-105. | Zbl 0258.46039

[00002] [Ł1] G. Łysik, Generalized analytic functions and a strong quasi-analyticity principle, Dissertationes Math. 340 (1995), 195-200. | Zbl 0882.46018

[00003] [Ł2] G. Łysik, Laplace ultradistributions on a half line and a strong quasi-analyticity principle, Ann. Polon. Math. 63 (1996), 13-33. | Zbl 0843.46025

[00004] [M] S. Mandelbrojt, Séries adhérentes, régularisation des suites, applications, Gauthier-Villars, Paris, 1952. | Zbl 0048.05203

[00005] [R] C. Roumieu, Sur quelques extensions de la notion de distribution, Ann. Sci. École Norm. Sup. 77 (1960), 41-121. | Zbl 0104.33403

[00006] [SZ] Z. Szmydt and B. Ziemian, The Laplace distributions on ℝ+n, submitted to J. Math. Sci. Univ. Tokyo.

[00007] [T] J. C. Tougeron, Gevrey expansions and applications, preprint, University of Toronto, 1991.

[00008] [W] D. V. Widder, The Laplace Transform, Princeton Univ. Press, Princeton, N.J., 1946. | Zbl 0060.24801

[00009] [Z] A. H. Zemanian, Generalized Integral Transformations, Interscience, 1969. | Zbl 0181.12701