Theory of relativistic heat polynomials and one-sided Lévy distributions

Abstract

The theory of pseudo-differential operators is a powerful tool to deal with differential equations involving differential operators under the square root sign. These type of equations are pivotal elements to treat problems in anomalous diffusion and in relativistic quantum mechanics. In this paper we report on new and unsuspected links between fractional diffusion, quantum relativistic equations and particular families of polynomials, linked to the Carlitz family, and playing the role of relativistic heat polynomials. We introduce generalizations of these polynomial families and point out their specific use for the solutions of problems of practical importance.

Typos corrected, references added

References in corpus (5)

• Exact and explicit probability densities for one-sided Levy stable distributions
• Relativistic equations with fractional and pseudo-differential operators
• Relativistic Wave Equations: An Operational Approach
• On the properties of Laplace transform originating from one-sided Lévy stable laws
• Relativistic dynamics, Green function and pseudodifferential operators

Cited by in corpus (4)

• Anomalous diffusion, non-Gaussianity, and nonergodicity for subordinated fractional Brownian motion with a drift
• Operational Methods in the Study of Sobolev-Jacobi Polynomials
• Relativistic Wave Equations on the lattice: an operational perspective
• Relativistic Heat Equation via Lévy stable distributions: Exact Solutions