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.
@article{bwmeta1.element.bwnjournal-article-apmv63z1p13bwm, author = {Grzegorz \L ysik}, title = {Laplace ultradistributions on a half line and a strong quasi-analyticity principle}, journal = {Annales Polonici Mathematici}, volume = {63}, year = {1996}, pages = {13-33}, zbl = {0843.46025}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv63z1p13bwm} }
Grzegorz Łysik. Laplace ultradistributions on a half line and a strong quasi-analyticity principle. Annales Polonici Mathematici, Tome 63 (1996) pp. 13-33. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv63z1p13bwm/
[000] [1] E. Hille, Analytic Function Theory, Vol. 2, Chelsea, New York, 1962. | Zbl 0102.29401
[001] [2] H. Komatsu, Ultradistributions, I. Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo 20 (1973), 25-105. | Zbl 0258.46039
[002] [3] H. Komatsu, Ultradistributions, II. The kernel theorem and ultradistributions with support in a submanifold, J. Fac. Sci. Univ. Tokyo 24 (1977), 607-628. | Zbl 0385.46027
[003] [4] M. Langenbruch, Bases in spaces of ultradifferentiable functions with compact support, Math. Ann. 281 (1988), 31-42. | Zbl 0627.46047
[004] [5] G. Łysik, Generalized analytic functions and a strong quasi-analyticity principle, Dissertationes Math. 340 (1995), 195-200. | Zbl 0882.46018
[005] [6] S. Mandelbrojt, Séries adhérentes, régularisation de suites, applications, Gauthier-Villars, Paris, 1952. | Zbl 0048.05203
[006] [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. | Zbl 0696.46001
[007] [8] M. Morimoto, Analytic functionals with non-compact carrier, Tokyo J. Math. 1 (1978), 77-103. | Zbl 0384.46027
[008] [9] S. Pilipović, Tempered ultradistributions, Boll. Un. Mat. Ital. B (7) 2 (1988), 235-251. | Zbl 0657.46030
[009] [10] C. Roumieu, Ultra-distributions définies sur et sur certaines classes de variétés différentiables, J. Anal. Math. 10 (1962-63), 153-192. | Zbl 0122.34802
[010] [11] Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type Partial Differential Equations, Kluwer, Dordrecht, 1992. | Zbl 0771.35002
[011] [12] A. H. Zemanian, Generalized Integral Transformations, Interscience, 1969.
[012] [13] B. Ziemian, Generalized analytic functions, Dissertationes Math., to appear.