Two Function Families and Their Application to Hankel Transform of Heat Kernel
Abstract
In this paper, we study an asymptotic expansion of the heat kernel for a Laplace operator on a smooth Riemannian manifold without a boundary at enough small values of the proper time. The SeeleyDeWitt coefficients of this decomposition satisfy a set of recurrence relations, which we use to construct two function families of a special kind. Using these functions, we find the expansion of a heat kernel for the inverse Laplace operator for an arbitrary dimension of space. We show that the new functions have some important properties. For example, we can consider the Laplace operator on the function set as a shift one. Also we describe various applications useful in theoretical physics and, in particular, we find the decomposition of Green functions in terms of new functions.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.00294
 Bibcode:
 2021arXiv210600294I
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory
 EPrint:
 LaTeX, 20 pages, 3 figures