Hilbert Space Embeddings for Gelfand–Shilov and Pilipović Spaces

Chen, Yuanyuan; Signahl, Mikael; Toft, Joachim

doi:10.1007/978-3-319-51911-1_3

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Sequence and Function Spaces1

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2019

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“…There is another way in considering the test space which corresponds to that limiting Beurling case α = 1/2 and can be considered also for α < 1/2 (cf. [26,17,10,9]). We will not treat these cases in the current paper.…”

Section: Sequence and Function Spacesmentioning

confidence: 99%

Localization of Fréchet frames and expansion of generalized functions

Pilipović¹,

Stoeva²

2019

Preprint

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Matrix type operators with the off-diagonal decay of polynomial or sub-exponential types are revisited with weaker assumptions concerning row or column estimates, still giving the continuity results for the frame type operators. Such results are extended from Banach to Fréchet spaces. Moreover, the localization of Fréchet frames is used for the frame expansions of tempered distributions and a class of Beurling ultradistributions.

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Section: Sequence and Function Spacesmentioning

confidence: 99%

Localization of Fréchet frames and expansion of generalized functions

Pilipović¹,

Stoeva²

2019

Preprint

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Images of function and distribution spaces under the Bargmann transform

Toft

2016

J. Pseudo-Differ. Oper. Appl.

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154

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We consider a broad family of test function spaces and their dual (distribution) space. The family includes Gelfand-Shilov spaces, a family of test function spaces introduced by S. Pilipović. We deduce different characterizations of such spaces, especially under the Bargmann transform and the Short-time Fourier transform. The family also include a test function space, whose dual space is mapped by the Bargmann transform bijectively to the set of entire functions.2010 Mathematics Subject Classification. primary 46F05; 32A25; 32A36; secondary 35Q40; 30Gxx.

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Hilbert Space Embeddings for Gelfand–Shilov and Pilipović Spaces

Cited by 2 publications

References 2 publications

Localization of Fréchet frames and expansion of generalized functions

Localization of Fréchet frames and expansion of generalized functions

Images of function and distribution spaces under the Bargmann transform

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