Hypergeometric reproducing kernels and analytic continuation from a half-line
Complex Variables
2007-05-23 v2 Classical Analysis and ODEs
Abstract
Indefinite inner product spaces of entire functions and functions analytic inside a disk are considered and their completeness studied. Spaces induced by the rotation invariant reproducing kernels in the form of the generalized hypergeometric function are completely characterized. A particular space generated by the modified Bessel function kernel is utilized to derive an analytic continuation formula for functions on using the best approximation theorem of S. Saitoh. As a by-product several new area integrals involving Bessel functions are explicitly evaluated
Cite
@article{arxiv.math/9908129,
title = {Hypergeometric reproducing kernels and analytic continuation from a half-line},
author = {Dmitry B. Karp},
journal= {arXiv preprint arXiv:math/9908129},
year = {2007}
}