Fourier transforms of rapidly decreasing functions on Rn
Abstract
With help of a certain family H of separately radial convex functions in Rn two new spaces of rapidly decreasing infinitely differentiable functions in Rn are introduced in the article. One of them, namely, the space G(H), is a subspace of Gelfand-Shilov type space Sα,A, where α = (1, . . . , 1) ∈ Rn,A = (0, . . . , 0) ∈ Rn. Functions of the second space E(H) admit an extension to entire functions in Cn. A description of the space of such extensions is obtained. Under some mild additional restrictions on H an isomorphism between the spaces G(H) and E(H) is established via the Fourier transform
About the Author
I. Kh. Musin
Institute of Mathematics with Computing Centre, Subdivision of the Ufa Federal Research Centre of the
Russian Academy of Sciences
Russian Federation
Russian Federation
112 Chernyshevsky str., Ufa 450008
References
1. I. M. Gel’fand, G. E. Shilov, Generalized Functions, V. 2: Spaces of Fundamental and Generalized Functions, AMS, Providence, R.I., 2016.
2. R.T. Rockafellar, Convex analysis, Princeton University Press, 1970.
3. M.A. Solov’ev, Spacelike asymptotic behavior of vacuum expectation values in nonlocal field theory, Theoret. and Math. Phys. 52 (3), 854–862 (1982). DOI: https://doi.org/10.1007/BF01038079
Review
For citations:
Musin I.Kh. Fourier transforms of rapidly decreasing functions on Rn. Mathematics and Theoretical Computer Science. 2023;1(2):12-21. (In Russ.)
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