Certificates of Positivity for Real Polynomials

2021 ◽  
Author(s):  
Victoria Powers
Keyword(s):  
Real Polynomials

scholarly journals On realizability of sign patterns by real polynomials

2018 ◽  
Vol 68 (3) ◽  
pp. 853-874 ◽  
Author(s):  
Vladimir Kostov
Keyword(s):  
Real Polynomials ◽  
Sign Patterns

Counting Critical Points of Real Polynomials in Two Variables

1993 ◽  
Vol 100 (3) ◽  
pp. 255 ◽  
Author(s):  
Alan Durfee ◽  
Nathan Kronefeld ◽  
Heidi Munson ◽  
Jeff Roy ◽  
Ina Westby
Keyword(s):  
Critical Points ◽  
Real Polynomials

On Newton's Inequality for Real Polynomials

1969 ◽  
Vol 76 (8) ◽  
pp. 905-909 ◽  
Author(s):  
J. N. Whiteley
Keyword(s):  
Real Polynomials

The arithmetic of certain semigroups of positive operators

1968 ◽  
Vol 64 (1) ◽  
pp. 161-166 ◽  
Author(s):  
John Lamperti
Keyword(s):  
Finite Number ◽  
Positive Definite ◽  
Positive Operators ◽  
Linear Operators ◽  
Real Numbers ◽  
Ultraspherical Polynomials ◽  
Real Polynomials ◽  
Fixed Parameter ◽  
Summation Sign ◽  
Image Position

Some time ago, S. Bochner gave an interesting analysis of certain positive operators which are associated with the ultraspherical polynomials (1,2). Let {Pn(x)} denote these polynomials, which are orthogonal on [ − 1, 1 ] with respect to the measureand which are normalized by settigng Pn(1) = 1. (The fixed parameter γ will not be explicitly shown.) A sequence t = {tn} of real numbers is said to be ‘positive definite’, which we will indicate by writing , provided thatHere the coefficients an 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 {Pn(x)}, and noting that

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