Paley-Wiener-type theorem for polynomial ultradifferentiable functions

Sharyn, S. V.

doi:10.15330/cmp.7.2.271-279

Cited by 2 publications

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“…where r H := ř into algebra { r H, •}. On the other hand, results of the article [13] imply that there exists a homomorphism F ⊗ : Γ(G β ) −→ Γ(E β ). Therefore, the map F • (F ⊗ ) −1 : Γ(E β ) −→ r H we may treat as "elementary" functional calculus.…”

Section: Functional Calculus For Countable Set Of Operatorsmentioning

confidence: 99%

Operator calculus for noncommuting operators over symmetric Fock space

Sharyn¹

2017

ijma

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In this paper we construct an operator calculus over the symmetric Fock space for countable set of noncommuting generators of strongly continuous groups, acting on a Hilbert space. As a symbol class of the calculus we use some algebra of functions of infinitely many variables. This algebra is described as the image of the space of polynomial ultradifferentiable functions under Fourier-Laplace transformation.

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Section: Functional Calculus For Countable Set Of Operatorsmentioning

confidence: 99%

Operator calculus for noncommuting operators over symmetric Fock space

Sharyn¹

2017

ijma

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“…In [5,15] the Fourier and Laplace transformations on the space of polynomial ultradistributions are considered, in [15] an appropriate Paley-Wiener-type theorem is proved.…”

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confidence: 99%

Algebraic and differential properties of polynomial Fourier transformation

Sharyn

2020

Mat. Stud.

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Methods of integral transformations of (generalized) functions are widely used in the solution of initial and boundary value problems for partial differential equations. However, many problems in applied mathematics require a nonlinear generalization of distribution spaces. Besides, an algebraic structure of a space of distributions is desirable, which is needed, for example, in quantum field theory.In the article, we use the adjoint operator method as well as technique of symmetric tensor products to extended the Fourier transformation onto the spaces of so-called polynomial rapidly decreasing test functions and polynomial tempered distributions. In such spaces it is possible to solve some Cauchy problems, for example, infinite dimensional heat equation associated with the Gross Laplacian.Algebraic and differential properties of the polynomial Fourier transformation are investigated. We prove some analogical to classical properties of this map. Unlike to the classic case, the spaces of polynomial test and generalized functions have algebraic structure. We prove that polynomial Fourier transformation acts as homomorphism of appropriate algebras. It is clear that the classical analogue of such property is absent.

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Paley-Wiener-type theorem for polynomial ultradifferentiable functions

Abstract: The image of the space of ultradifferentiable functions with compact supports under Fourier-Laplace transformation is described. An analogue of Paley-Wiener theorem for polynomial ultradifferentiable functions is proved.

Cited by 2 publications

References 4 publications

Operator calculus for noncommuting operators over symmetric Fock space

Operator calculus for noncommuting operators over symmetric Fock space

Algebraic and differential properties of polynomial Fourier transformation

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