Advertisement

Convolutions of Generating Operators

  • Semen B. Yakubovich
  • Yurii F. Luchko
Part of the Mathematics and Its Applications book series (MAIA, volume 287)

Abstract

We considered convolutions of the generalized H-transforms in Chapter 11. The main property of these convolutions is the following {fy205-1} where (H a f)(x) is the generalized H-transform with the power weight (11.1). It follows from this relation that the H-convolution (f * a )(x) is connected with some integral transform and this connection is reflected in the names of other convolutions (Laplace convolution, Mellin convolution, et c.). A different approach to the definition of convolution, which connects some other operator with a convolution has been proposed by I.H. Dimovski ((1966)–(1981)). His definition is more suitable in developing a Mikusinski type operational calculus. In this chapter we will deal with convolutions in the Dimovski’s sense.

Keywords

Linear Operator Integration Operator Linear Space Generate Operator Main Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • Semen B. Yakubovich
    • 1
  • Yurii F. Luchko
    • 1
  1. 1.Department of Mathematics and MechanicsBeylorussian State UniversityMinsk, ByelorussiaRussia

Personalised recommendations