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- W2466524684 abstract "We characterize the images of the Gelfand-Shilov spaces and their distribution spaces under the Bargmann transform. The aim of the paper is to deduce mapping properties of the Bargmann transform between Gelfand-Shilov spaces and their dual spaces, spaces of Gelfand-Shilov distributions of certain degrees, to convenient sets of entire functions. We also deduce certain duality properties between these dual spaces. We apply these results to characterize the Gelfand- Shilov spaces and their distribution spaces, in terms of short-time Fourier transforms and to show that all these function and distribution spaces are obtained by suitable unions or intersections of the broad family of modulation spaces, introduced in (14). We remark that less general versions of the results here can be found in (14) and to some extent in (3), where similar investigations can be found. Especially we note that our results here include situations valid for the Gelfand-Shilov space S s t and their distribution space (S s t ) ' for s,t ≥ 1/2, while the largest part of the analysis in (3,14) require that s,t > 1/2, which do not include the limit cases s = 1/2 or t = 1/2. We also use the result to characterize the Gelfand-Shilov spaces in terms of the short-time Fourier transform, in a similar way as in (14). In fact, let s,t > 0 be such that" @default.
- W2466524684 created "2016-07-22" @default.
- W2466524684 creator A5015710179 @default.
- W2466524684 date "2014-09-18" @default.
- W2466524684 modified "2023-09-27" @default.
- W2466524684 title "THE IMAGES OF GELFAND-SHILOV SPACES UNDER THE BARGMANN TRANSFORM" @default.
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