Schur-SzegA composition of entire functions

Dimitrov, Dimitar Kolev [UNESP]; Kostov, Vladimir P.

Schur-SzegA composition of entire functions

Data

2012-07-01

Autores

Dimitrov, Dimitar Kolev

Kostov, Vladimir P.

Editor

Springer

Tipo

Artigo

Direito de acesso

Acesso restrito

Resumo

For any pair of algebraic polynomials A(x) = Sigma(n)(k=0) ((n)(k))a(k)x(k) and B(x) = Sigma(n)(k=0) ((n)(k))b(k)x(k), their Schur-Szego composition is defined by (A (*)(n) B)(x) = Sigma(n)(k=0) ((n)(k))a(k)b(k)x(k). Motivated by some recent results which show that every polynomial P(x) of degree n with P(-1) = 0 can be represented as K-a1 (*)(n) ... (*)(n) Kan-1 with K-a := (x + 1)(n-1) (x + a), we introduce the notion of Schur-Szego composition of formal power series and study its properties in the case when the series represents an entire function. We also concentrate on the special case of composition of functions of the form e(x) P(x), where P(x) is an algebraic polynomial and investigate its properties in detail.