Composition method for constructing convolutions for integral transforms

Convolutions for the Fourier transforms with geometric variables and applications

“…The generalized convolutions for integral transforms and their applications were first studied by Churchill in 1941, then the idea of construction of convolutions was formulated by Vilenkin in 1958 (see [7,9,33]). In 1967, the construction methods for generalized convolutions of arbitrary integral transforms were proposed by Kakichev, and in 1990 the concept of generalized convolutions for linear operators was introduced by the same author (see [19,20]). In 1997, some convolutions for integral transforms were obtained, and in 1998 the generalized convolutions for the Fourier-cosine and Fourier-sine integral transforms were presented (see [21,22]).…”

“…Generally speaking, each of the convolutions is a new transform which has become an object of study (see [1,19]). In our view, the integral transforms of Fourier type deserve special interest.…”

The Hermite Functions Related to Infinite Series of Generalized Convolutions and Applications

“…Generalized convolution with weight-function is a nice idea based on the so-called factorization identity (see [11,13,16]). The following theorem presents the generalized convolutions with Hermitian weight-function.…”

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

“…One reason for this is that they have many applications in pure and applied mathematics (see ), Vladimirov [23] and references therein). Each convolution is a new transform which can be an object of study (see [4,5,6,10,20,21,22]). Moreover, convolution is a mathematical way of combining two signals to form a third signal, which is a very important technique in digital signal processing (see Smith [14]).…”