Inverse functions of polynomials and orthogonal polynomials as operator monotone functions
Author:
Mitsuru Uchiyama
Journal:
Trans. Amer. Math. Soc. 355 (2003), 41114123
MSC (2000):
Primary 47A63, 15A48; Secondary 33C45, 30B40
Published electronically:
June 10, 2003
MathSciNet review:
1990577
Fulltext PDF Free Access
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Abstract: We study the operator monotonicity of the inverse of every polynomial with a positive leading coefficient. Let be a sequence of orthonormal polynomials and the restriction of to , where is the maximum zero of . Then and the composite 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 semioperator monotone, that is, for matrices , implies
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Additional Information
Mitsuru Uchiyama
Affiliation:
Department of Mathematics, Fukuoka University of Education, Munakata, Fukuoka, 8114192, Japan
Email:
uchiyama@fukuokaedu.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002994703033555
PII:
S 00029947(03)033555
Keywords:
Positive semidefinite operator,
operator monotone function,
orthogonal polynomials
Received by editor(s):
October 16, 2002
Published electronically:
June 10, 2003
Article copyright:
© Copyright 2003 American Mathematical Society
