Comparison theorem between Fourier transform and Fourier transform with compact support

Christine Huyghe

Displaying similar documents to “Comparison theorem between Fourier transform and Fourier transform with compact support”

Operational calculus and Fourier transform on Boehmians

V. Karunakaran, R. Roopkumar (2005)

Colloquium Mathematicae

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We define various operations on the space of ultra Boehmians like multiplication with certain analytic functions which are Fourier transforms of compactly supported distributions, polynomials, and characters $(e^{i s t}, s, t \in ℝ)$ , translation, differentiation. We also prove that the Fourier transform on the space of ultra Boehmians has all the operational properties as in the classical theory.

A stable method for the inversion of the Fourier transform in $R^{N}$

Leonede De Michele, Delfina Roux (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A general method is given for recovering a function $f : R^{N} \to C$ , $N \geq 1$ , knowing only an approximation of its Fourier transform.

Uncertainty principles for integral operators

Saifallah Ghobber, Philippe Jaming (2014)

Studia Mathematica

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The aim of this paper is to prove new uncertainty principles for integral operators with bounded kernel for which there is a Plancherel Theorem. The first of these results is an extension of Faris’s local uncertainty principle which states that if a nonzero function $f \in L ² (ℝ^{d}, μ)$ is highly localized near a single point then (f) cannot be concentrated in a set of finite measure. The second result extends the Benedicks-Amrein-Berthier uncertainty principle and states that a nonzero function $f \in L ² (ℝ^{d}, μ)$ and...

Absolute convergence of multiple Fourier integrals

Yurii Kolomoitsev, Elijah Liflyand (2013)

Studia Mathematica

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Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained. The results are given in terms of $L_{p}$ integrability of the function and its partial derivatives, each with a different p. These p are subject to certain relations known earlier only for some particular cases. Sharpness and applications of the results obtained are also discussed.

Boehmians of type S and their Fourier transforms

R. Bhuvaneswari, V. Karunakaran (2010)

Annales UMCS, Mathematica

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Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.

Boehmians of type S and their Fourier transforms

R. Bhuvaneswari, V. Karunakaran (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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On the Hausdorff-Young theorem for commutative hypergroups

Sina Degenfeld-Schonburg (2013)

Colloquium Mathematicae

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We study the Hausdorff-Young transform for a commutative hypergroup K and its dual space K̂ by extending the domain of the Fourier transform so as to encompass all functions in $L^{p} (K, m)$ and $L^{p} (K ̂, π)$ respectively, where 1 ≤ p ≤ 2. Our main theorem is that those extended transforms are inverse to each other. In contrast to the group case, this is not obvious, since the dual space K̂ is in general not a hypergroup itself.

Rearrangement of coefficients of Fourier series on $S U_{2}$

Giancarlo Travaglini (1987)

Colloquium Mathematicae

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The Fourier transform in Lebesgue spaces

Erik Talvila (2025)

Czechoslovak Mathematical Journal

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For each $f \in L^{p} (ℝ)$ ( $1 \leq p < \infty$ ) it is shown that the Fourier transform is the distributional derivative of a Hölder continuous function. For each $p$ , a norm is defined so that the space of Fourier transforms is isometrically isomorphic to $L^{p} (ℝ)$ . There is an exchange theorem and inversion in norm.

Small sets in the support of a Fourier-Stieltjes transform

Louis Pigno (1981)

Colloquium Mathematicae

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A remark on Fourier-Stieltjes transform

S. Hartman (1975)

Colloquium Mathematicae

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Non-Sidon sets in the support of a Fourier-Stieltjes transform

Colin C. Graham (1976)

Colloquium Mathematicae

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Sidon sets and $I^{0}$ -sets

David Grow (1987)

Colloquium Mathematicae

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Inverse Fourier transform

Leonede De Michele, Marina Di Natale, Delfina Roux (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this paper a very general method is given in order to reconstruct a periodic function $f$ knowing only an approximation of its Fourier coefficients.

On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms

Yujiao Jiang, Guangshi Lü (2014)

Acta Arithmetica

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Let $λ_{f} (n)$ be the nth normalized Fourier coefficient of a holomorphic or Maass cusp form f for SL(2,ℤ). We establish the asymptotic formula for the summatory function $\sum_{\begin{matrix} n \leq x \\ n \equiv l (m o d q) \end{matrix}} {| λ_{f} (n) |}^{2 j}$ as x → ∞, where q grows with x in a definite way and j = 2,3,4.

Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space

Jae Gil Choi, Sang Kil Shim (2023)

Czechoslovak Mathematical Journal

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We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space $(H, B, ν)$ . An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space $B$ . Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in...