Gelfand–Shilov space

In the mathematical field of <a href="/facts/Functional_analysis/MIp233MT">functional analysis</a>, a Gelfand–Shilov space 
 
 
 
 
 S
 
 α
 
 
 β
 
 
 
 
 {\displaystyle S_{\alpha }^{\beta }}
 
 is a space of <a href="/facts/Test_function/yfaJ4mUp">test functions</a> for the theory of <a href="/facts/Generalized_function/fCM4VsyT">generalized functions</a>, introduced by <a href="/facts/Israel_Gelfand/TJeJouKs">Gelfand</a> and <a href="/facts/Georgii_Evgen%2527evich_Shilov/jBxVRhkK"> Shilov</a> (1968, Chapter IV).

<ul><li>Chung, Jaeyoung; Chung, Soon-Yeong; Kim, Dohan (1996), "Characterizations of the Gel'fand–Shilov spaces via Fourier transforms", <a href="/facts/Proceedings_of_the_American_Mathematical_Society/W3wRF3MV">Proceedings of the American Mathematical Society</a>, 124 (7): 2101–2108, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1090%2FS0002-9939-96-03291-1">10.1090/S0002-9939-96-03291-1</a>, <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0002-9939">0002-9939</a>, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=1322917">1322917</a></li>
<li>Gelfand, I. M.; Shilov, G. E. (1968) [1958], Generalized functions. Vol. 2. Spaces of fundamental and generalized functions, vol. 2, Boston, MA: <a href="/facts/Academic_Press/qxoKjzFy">Academic Press</a>, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0230128">0230128</a></li></ul>

Gelfand–Shilov space open-in-new

Gelfand–Shilov space