Fourier transforms of convolution operators

Integral Transforms of Fourier Cosine Convolution Type

which has the following property Fc(f ∗ g)(x) = (Fcf)(x)(Fcg)(x). (3) The theory of integral transforms related to the Fourier and Mellin convolutions is well developed [2, 6, 10, 11, 12, 13, 19] and has many applications. Some other classes of integral transforms, that are not related to any known convolutions, are considered in [14, 15]. In this paper we investigate integral transforms of the...

Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type

Appendix: Fourier transforms and shift-invariant linear operators

THREE CLASSES OF PERCEPTUAL PHENOMENA can be thoroughly explained in physiological terms at the present time? This introductory section surveys the overall status of physiological explanations of visual phenomena. At present, tight explanatory links between perception and physiology are still largely confined to the level of the optics of the retinal image and its initial neural registration by...

Continuityof Operators Intertwiningwith Convolution Operators

Let G be a locally compact abelian group, let m be a bounded complex-valued Borel measure on G; and let Tm be the corresponding convolution operator on LðGÞ: Let X be a Banach space and let S be a continuous linear operator on X : Then we show that every linear operator F : X ! LðGÞ such that FS 1⁄4 TmF is continuous if and only if the pair ðS;TmÞ has no critical eigenvalue. # 2002 Elsevier Sci...

Domains of holomorphy for Fourier transforms of solutions to discrete convolution equations

We study solutions to convolution equations for functions with discrete support in R, a special case being functions with support in the integer points. The Fourier transform of a solution can be extended to a holomorphic function in some domains in C, and we determine possible domains in terms of the properties of the convolution operator.