The arithmetic of certain semigroups of positive operators

Content Provider	Scilit
Author	Lamperti, John
Copyright Year	1968
Description	Some time ago, S. Bochner gave an interesting analysis of certain positive operators which are associated with the ultraspherical polynomials (1,2). Let ${P_{n}$(x)} denote these polynomials, which are orthogonal on [ − 1, 1 ] with respect to the measure and which are normalized by settigng $P_{n}$(1) = 1. (The fixed parameter γ will not be explicitly shown.) A sequence t = ${t_{n}$} of real numbers is said to be ‘positive definite’, which we will indicate by writing , provided that Here the coefficients $a_{n}$ are real, and the prime on the summation sign means that only a finite number of terms are different from 0. This condition can be rephrased by considering the set of linear operators on the space of real polynomials which have diagonal matrices with respect to the basis ${P_{n}$(x)}, and noting that
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9C94BB5068D2497CC437B26B181FEC16/S0305004100042675a.pdf/div-class-title-the-arithmetic-of-certain-semigroups-of-positive-operators-div.pdf
Ending Page	166
Page Count	6
Starting Page	161
ISSN	03050041
e-ISSN	14698064
DOI	10.1017/s0305004100042675
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Issue Number	1
Volume Number	64
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	1968-01-01
Access Restriction	Open
Subject Keyword	Mathematical Proceedings of the Cambridge Philosophical Society Applied Mathematics Positive Operators
Content Type	Text
Resource Type	Article
Subject	Mathematics