Artigo
Schur-SzegA composition of entire functions
Fecha
2012-07-01Registro en:
Revista Matematica Complutense. New York: Springer, v. 25, n. 2, p. 475-491, 2012.
1139-1138
10.1007/s13163-011-0078-3
WOS:000305478800007
1681267716971253
Autor
Univ Nice
Universidade Estadual Paulista (Unesp)
Resumen
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.