A mapping connected with the Schur–Szegő composition

Kostov, Vladimir Petrov

doi:10.1016/j.crma.2009.10.025

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Properties Of the Schur-szegő Composition1

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2012

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“…For k = 0, Remark 6 in [4] states that in the case of a polynomial P there are at least m different negative among the numbers a i . In the case of a polynomial R the same statement is contained in Corollary 2 in [8].…”

Section: Properties Of the Schur-szegő Compositionmentioning

confidence: 73%

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A refined realization theorem in the context of the Schur–Szegő composition

Kostov

2012

Bulletin des Sciences Mathématiques

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Every polynomial of the form P = (x + 1)(x n−1 + c 1 x n−2 + · · · + c n−1 ) is representable as Schur-Szegő composition of n − 1 polynomials of the form (x + 1) n−1 (x + a i ), where the numbers a i are unique up to permutation. We give necessary and sufficient conditions upon the possible values of the 8-vector whose components are the number of positive, zero, negative and complex roots of a real polynomial P and the number of positive, zero, negative and complex among the quantities a i corresponding to P . A similar result is proved about entire functions of the form e x R, where R is a polynomial.2000 Mathematics Subject Classification. Primary 12A10 Secondary 30D99.

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Section: Properties Of the Schur-szegő Compositionmentioning

confidence: 73%

“…The mapping Φ is affine non-degenerate (see [1]) and its eigenvalues are rational positive numbers (see [3]). For other properties of this mapping see [5] and [10]. Denote in the case of a real polynomial P by ρ the number of the real roots of the polynomial P/(x + 1) and by r the number of the real among the quantities a i .…”

mentioning

confidence: 99%

A refined realization theorem in the context of the Schur–Szegő composition

Kostov

2012

Bulletin des Sciences Mathématiques

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show abstract

A mapping connected with the Schur–Szegő composition

Cited by 1 publication

References 5 publications

A refined realization theorem in the context of the Schur–Szegő composition

A refined realization theorem in the context of the Schur–Szegő composition

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