Displaying similar documents to “Fourier-like kernels as solutions of ODE's.”

On the Fourier transform of the symmetric decreasing rearrangements

Philippe Jaming (2011)

Annales de l’institut Fourier

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Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the L 2 behavior of a Fourier transform of a function over a small set is controlled by the L 2 behavior of the Fourier transform of its symmetric decreasing rearrangement. In the L 1 case, the same is true if we further assume that the function has a support of finite measure. As...

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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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.

On bilinear Littlewood-Paley square functions.

Michael T. Lacey (1996)

Publicacions Matemàtiques

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On the real line, let the Fourier transform of kn be k'n(ξ) = k'(ξ-n) where k'(ξ) is a smooth compactly supported function. Consider the bilinear operators Sn(f, g)(x) = ∫ f(x+y)g(x-y)kn(y) dy. If 2 ≤ p, q ≤ ∞, with 1/p + 1/q = 1/2, I prove that Σ∞ n=-∞ ||Sn(f,g)||2 2...