The two-sided Laplace transformation over the Cayley-Dickson algebras and its applications
S. V. Ludkovsky
Abstract
This article is devoted to the noncommutative version of the Laplace transformation. New types of the direct and inverse transformations of the Laplace type over general Cayley-Dickson algebras, in particular, also the skew field of quaternions and the octonion algebra are investigated. Examples are given. Theorems are proved about properties of such transformations and also theorems about images and originals in conjunction with operations of multiplication, differentiation, integration, convolution, shift and homothety. The noncommutative analog of the Mellin transformation is studied as well. Applications are given to solutions of differential equations over the Cayley-Dickson algebras.
Create a lesson
Related papers
Square Functions and the Complete Crouzeix Conjecture in Dimension Three
Per Åhag, Rafał Czyż, Antti Perälä et al.
On the Levi map of nondegenerate CR submanifolds
Florian Bertrand, Francine Meylan
Smale's Mean Value Conjecture and its Dual Conjecture for Complex Polynomials
Aneesh Jatar, Tuen Wai Ng
Transcendental Numerical Dimension and Rational Quotients in Kähler Geometry
Songchen Liu
Compactness and the essential norm on Bergman spaces of the Siegel upper half-space
Peiyao Li, Congwen Liu, Jiajia Si
Existence of a "maximal" domain of meromorphy for an analytic function outside a polar compact set
Aleksandr Komlov