Gelfand–Shilov Type Spaces Through Hermite Expansions

Gramchev, Todor; Lecke, Alexander; Pilipović, Stevan; Rodino, Luigi

doi:10.1007/978-3-319-14618-8_8

Cited by 10 publications

(5 citation statements)

References 12 publications

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“…Proof. We use the Hermite functions It is known that Gelfand-Shilov spaces and their distribution duals can be identified by means of such series expansions, with characterizations in terms of the corresponding sequence spaces (see [14,15,38] and the references therein).…”

Section: Appendixmentioning

confidence: 99%

The Weyl product on quasi-Banach modulation spaces

2018

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Section: Appendixmentioning

confidence: 99%

The Weyl product on quasi-Banach modulation spaces

2018

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“…Gelfand-Shilov spaces and their ultradistribution duals, as well as the Schwartz space S and the tempered distributions S ′ , and L 2 , can be identified by means of such series expansions, with characterizations in terms of the corresponding sequence spaces (see [7,6,22,28]). Let…”

Section: Preliminariesmentioning

confidence: 99%

Semigroups for quadratic evolution equations acting on Shubin–Sobolev and Gelfand–Shilov spaces

Wahlberg

2022

Ann. Fenn. Math.

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We consider the initial value Cauchy problem for a class of evolution equations whose Hamiltonian is the Weyl quantization of a homogeneous quadratic form with non-negative definite real part. The solution semigroup is shown to be strongly continuous on several spaces: the Shubin-Sobolev spaces, the Schwartz space, the tempered distributions, the equal index Beurling type Gelfand-Shilov spaces and their dual ultradistribution spaces.

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“…Gelfand-Shilov spaces and their distribution duals, as well as the Schwartz space S and the tempered distributions S ′ , can be identified by means of such series expansions, with characterizations in terms of the corresponding sequence spaces (see [4,5,16,20] [20,Theorem V.13] showed that the family of Hilbert sequence spaces…”

Section: Preliminariesmentioning

confidence: 99%

Semigroups for quadratic evolution equations acting on Shubin-Sobolev and Gelfand-Shilov spaces

Wahlberg¹

2019

Preprint

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We consider the initial value Cauchy problem for a class of evolution equations whose Hamiltonian is the Weyl quantization of a homogeneous quadratic form with non-negative definite real part. The solution semigroup is shown to be strongly continuous on several spaces: the Shubin-Sobolev spaces, the Schwartz space, the tempered distributions, the Beurling type Gelfand-Shilov spaces and their dual ultradistribution spaces.

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Gelfand–Shilov Type Spaces Through Hermite Expansions

Abstract: Abstract. Gelfand-Shilov spaces of the type S α α (R d ) and α α (R d ) can be realized as sequence spaces by means of the Hermite representation Theorem. In this article we show that for a function, where 1 2 ≤ α ≤ β (resp.

Cited by 10 publications

References 12 publications

The Weyl product on quasi-Banach modulation spaces

The Weyl product on quasi-Banach modulation spaces

Semigroups for quadratic evolution equations acting on Shubin–Sobolev and Gelfand–Shilov spaces

Semigroups for quadratic evolution equations acting on Shubin-Sobolev and Gelfand-Shilov spaces

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