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Fractional Fourier transform for space–time algebra-valued functions
The aim of this article is to introduce a fractional space–time Fourier transform (FrSFT) by generalizing the fractional Fourier transform for...
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On the boundedness of multilinear Fourier multipliers on Hardy spaces
In this paper, we study multilinear Fourier multiplier operators on Hardy spaces. In particular, we prove that the multilinear Fourier multiplier...
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Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems
Fourier continuation (FC) is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions....
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Fast Fourier Transforms for Nonequispaced Data
In this chapter, we describe fast algorithms for the computation of the DFT for d-variate nonequispaced data, since in a variety of applications the...
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A Note on Carleson-Hunt Type Theorems for Vilenkin-Fourier Series
In this paper we discuss an analogy of the Carleson-Hunt theorem with respect to Vilenkin systems. In particular, we investigate the almost...
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Restriction theorem for the Fourier–Dunkl transform I: cone surface
In this article, we define the Fourier–Dunkl transform, which generalizes the Fourier transform. We prove Strichartz’s restriction theorem for the...
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The Fourier Transform for Sheaves and Cycles
For abelian varieties one knows a little more about algebraic cycles than for most other classes of smooth projective varieties. This is mainly due...
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Rough pseudodifferential operators on Hardy spaces for Fourier integral operators
We prove map** properties of pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols a ( x,η ) are...
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Littlewood-Paley Theorem, Nikolskii Inequality, Besov Spaces, Fourier and Spectral Multipliers on Graded Lie Groups
In this paper we investigate Besov spaces on graded Lie groups. We prove a Nikolskii type inequality (or the Reverse Hölder inequality) on graded Lie...
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Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces
This work deals with the extension problem for the fractional Laplacian on Riemannian symmetric spaces G / K of noncompact type and of general rank,...
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Graph Fourier transform based on singular value decomposition of the directed Laplacian
The Graph Fourier transform (GFT) is a fundamental tool in graph signal processing. In this paper, based on singular value decomposition of the...
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Chapter 3: Pseudo-Differential Operators and Fourier Operators
In 1807, Jean-Baptiste Fourier had his say in the famous (going from the beginning of the XVIII century) dispute about the sounding string...