MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
A basis property of families of the Mittag-Leffler functions
Milutin Dostanić

Abstract

In this paper we study basis properties of the Mittag-Leffler functions $\{y(x,\lambda_k)\}$ where $$ y(x,\lambda)=|x|^{\omega/2}E_1(ix\lambda;1+\omega/2),\quad\omega\in(-1,1), $$ $E_1(z;\alpha)=\sum\limits_{k=0}^{\infty}\dfrac{z^k}{\Gamma(\alpha+k)}$ and $\{\lambda_k\}$ is a sequence of complex numbers. In the case $\omega=0$ this system is reduced to the exponential system.

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Keywords: Basis property, Riesz basis, Mittag-Leffler functions.

MSC: 30B60

Pages:  77--82     

Volume  48 ,  Issue  3$-$4 ,  1996