Schur-SzegA composition of entire functions
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Data
2012-07-01
Autores
Dimitrov, Dimitar Kolev [UNESP]
Kostov, Vladimir P.
Título da Revista
ISSN da Revista
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Editor
Springer
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.
Descrição
Palavras-chave
Schur-Szego composition, Entire functions, Hyperbolic polynomials, Laguerre-Polya class
Como citar
Revista Matematica Complutense. New York: Springer, v. 25, n. 2, p. 475-491, 2012.