COMPLETE SYSTEMS OF WEBER - HERMITE FUNCTIONS

Abstract

Let $\{ D_\nu(z) \}_{\nu \in C}$ be system of Weber - Hermite functions. It is proved that the system $(*)$ is complete in the space $L_2(-\infty, + \infty)$ if $0 < \omega < 4/3$ and $Re \sigma > -1/2$. The completeness of Hermite functions $(**)$ in the same space is a particular case $(\omega=1, \sigma=0)$