On weighted generalized functions associated with quadratic forms

Abstract

In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with Bessel operator.

16 pages

References in corpus (1)

• The solutions of the $n$-dimensional Bessel diamond operator and the Fourier--Bessel transform of their convolution

Cited by in corpus (1)

• The general form of the Euler--Poisson--Darboux equation and application of transmutation method