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 $(\ast )$ is complete in the space $L_2(-\mathrm{\infty },+\mathrm{\infty })$ if $0<\omega <4/3$ and $Re\sigma >-1/2$. The completeness of Hermite functions $(\ast \ast )$ in the same space is a particular case $(\omega =1,\sigma =0)$