Inversion formulas for the reznitskaya transform and stability of lipschitz type in determination of initial heat distribution

Abstract

In the Reznitskaya transform combining the solutions of some general linear partial differential equations of hyperbolic type and parabolic type, isometrical identities and inversion formulas are established. Furthermore, stability of Lipschitz type in the determination of initial heat distribution is given as an application.

Keywords:

• Reznitskaya transform
• pde
• Bergman—Selberg space
• reproducing kernel
• integral transform
• stability of Lipschitz type
• observability inequality
• inverse problem

AMS:

• 44A15
• 30C40
• 46E22
• 35B35