Ornstein-Uhlenbeck Semigroup on the dual space of Gelfand-Shilov Spaces of Beurling type
DOI:
https://doi.org/10.5269/bspm.40348Abstract
We use a previously obtained topological characterization of Gelfand-Shilov spaces of Beurling type to characterize its dual using Riesz representation theorem. Using the characterization of the dual space equipped with the weak topology, we study the action of Ornstein-Uhlenbeck Semigroup on the dual space.
References
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2. D. Gabor, Theory of communication, J. IEE (London), 93 (III): 429-457, November 1946.
3. H. Komatsu, Ultradistributions. I: Structure theorems and a characterization, J. Fac. Sei. Univ. Tokyo Sect. IA Math. 20 (1973), 25-105.
4. I. M. Gelfand and G. E. Shilov, Generalized functions, Vol. II, Academic Press. New York, 1964.
5. W. Rudin, Functional Analysis, Second Edition, McGraw-Hill Inc., 1991.
6. S. Pilipovic, Tempered ultradistributions, Boll. U.M.I. 7 (1988), 235-251.
7. S. Pilipovic, Characterization of bounded sets in spaces of ultradistributions, Proc. Amer. Math. Soc. 120 (1994), 1191-1206.
8. A. Kaminski, D. Perisic, S. Pilipovic, On the Convolution in the Gelfand-Shilov spaces, Integral Transforms and Special Functions, 4:1-2 (2007), 83-96, DOI: 10.1080/10652469608819096.
9. L. Schwartz, Une characterization de l’space S de Schwartz, C. R. Acad. Sci. Paris Ser. I 316 (1993) 23-25.
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2020-10-07
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