On the generalized convolution with a weight function for the Fourier sine and cosine transforms

Mathematische Nachrichten

2010

This paper gives a general formulation of convolutions for arbitrary linear operators from a linear space to a commutative algebra, constructs three convolutions for the Fourier transforms with geometric variables and four generalized convolutions for the Fourier-cosine, Fourier-sine transforms. With respect to applications, by using the constructed convolutions normed rings on L1(R n ) are constructed, and explicit solutions of integral equations of convolution type are obtained.

Section: Proposition 312mentioning

confidence: 99%

Convolutions for the Fourier transforms with geometric variables and applications

Giang

Mau

Mathematische Nachrichten

2010

“…b) There is an approach to integral equations of convolution type by using an appropriate convolution and the Wiener-Lèvy theorem as e.g. in [8,11,16,17]. However, that approach usually includes only sufficient conditions (no necessary conditions) for the solvability of the equations and obtains the solutions in implicit (not explicit) form.…”

Section: Partial Differential Equations and Integral Equations Of Conmentioning

confidence: 99%

Operational Properties of Two Integral Transforms of Fourier Type and their Convolutions

Giang

Mau

Integr. equ. oper. theory

2009

In this paper we present the operational properties of two integral transforms of Fourier type, provide the formulation of convolutions, and obtain eight new convolutions for those transforms. Moreover, we consider applications such as the construction of normed ring structures on L1(R), further applications to linear partial differential equations and an integral equation with a mixed Toeplitz-Hankel kernel. Mathematics Subject Classification (2000). Primary 42B10; Secondary 44A20, 44A35, 47G10.

“…and f ∈ L 1 (R + ), the generalized convolutions (1.8), (1.9) are well-defined and the following factorization properties hold (see [9,14])…”

Section: Preliminariesmentioning

confidence: 99%

“…The generalized convolutions of two functions h and f with a weight function γ(y) = e −y sin y for three transforms -the Fourier cosine, the Fourier and the Fourier sine integral transforms were studied in [9,14] (h…”

Section: Preliminariesmentioning

confidence: 99%

A Fourier generalized convolution transform and applications to integral equations

Thảo

Hong

2012

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