ON A BIORTOGONAL SYSTEM OF MUNTS FUNCTION

Abstract

Munts quazipolinomial orthogonal systems from the $\left\{ x^{\gamma_k}\right\} $ and $\left\{ e^{-\gamma_k x}\right\}$ $(\gamma_k$ are real numbers) have been for the first time derived in an integral representation by H.V. Badalian [1,2]. In the case of $\left\{ e^{-\gamma_k x}\right\}$ they are considered in the article as (2), which remains without change in a more general case for multiple $\gamma_k$.  In this connection the importance of developing a two power sequences based biorthogonal system is that together with the sequence  $\left\{e^{-\gamma_k x}\right\}$  it creates a possibility of free selection another sequence $\left\{e^{-\gamma_k x}\right\}$ simplifying the application of functions representation apparatus.