Gelfand–Shilov space

In the mathematical field of functional analysis, a Gelfand–Shilov space $S_{\alpha }^{\beta }$ is a space of test functions for the theory of generalized functions, introduced by Gelfand and Shilov (1968, Chapter IV).

References

Chung, Jaeyoung; Chung, Soon-Yeong; Kim, Dohan (1996), "Characterizations of the Gel'fand–Shilov spaces via Fourier transforms", Proceedings of the American Mathematical Society, 124 (7): 2101–2108, doi:10.1090/S0002-9939-96-03291-1, ISSN 0002-9939, MR 1322917
Gelfand, I. M.; Shilov, G. E. (1968) [1958], Generalized functions. Vol. 2. Spaces of fundamental and generalized functions, vol. 2, Boston, MA: Academic Press, MR 0230128

Functional analysis (topics – glossary)

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Banach Besov Fréchet Hilbert Hölder Nuclear Orlicz Schwartz Sobolev Topological vector
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v t e Topological vector spaces (TVSs)
Basic concepts	Banach space Completeness Continuous linear operator Linear functional Fréchet space Linear map Locally convex space Metrizability Operator topologies Topological vector space Vector space
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Types of TVSs	Asplund B-complete/Ptak Banach (Countably) Barrelled BK-space (Ultra-) Bornological Brauner Complete Convenient (DF)-space Distinguished F-space FK-AK space FK-space Fréchet tame Fréchet Grothendieck Hilbert Infrabarreled Interpolation space K-space LB-space LF-space Locally convex space Mackey (Pseudo)Metrizable Montel Quasibarrelled Quasi-complete Quasinormed (Polynomially Semi-) Reflexive Riesz Schwartz Semi-complete Smith Stereotype (B Strictly Uniformly) convex (Quasi-) Ultrabarrelled Uniformly smooth Webbed With the approximation property
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References