Inverse functions of polynomials and orthogonal polynomials as operator monotone functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Inverse functions of polynomials and orthogonal polynomials as operator monotone functions

Authors:	Mitsuru Uchiyama

Affiliation:	Department of Mathematics, Fukuoka University of Education, Munakata, Fukuoka, 811-4192, Japan

Abstract:	We study the operator monotonicity of the inverse of every polynomial with a positive leading coefficient. Let ${p_n}_{n=0}^{infty}$ be a sequence of orthonormal polynomials and $p_{n+}$ the restriction of to , where is the maximum zero of . Then $p_{n+}^{-1}$ and the composite $p_{n-1}circ p_{n+}^{-1}$ are operator monotone on . Furthermore, for every polynomial with a positive leading coefficient there is a real number so that the inverse function of defined on is semi-operator monotone, that is, for matrices , $(p(A+a)-p(a))^2 leq ((p(B+a)-p(a))^{2}$ implies

Keywords:	Positive semi-definite operator operator monotone function orthogonal polynomials

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