The extremal zeros of a perturbed orthogonal polynomials system
نویسندگان
چکیده
منابع مشابه
Applications of the monotonicity of extremal zeros of orthogonal polynomials in interlacing and optimization problems
We investigate monotonicity properties of extremal zeros of orthogonal polynomials depending on a parameter. Using a functional analysis method we prove the monotonicity of extreme zeros of associated Jacobi, associated Gegenbauer and q-Meixner-Pollaczek polynomials. We show how these results can be applied to prove interlacing of zeros of orthogonal polynomials with shifted parameters and to d...
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Monotonicity of zeros of orthogonal Laurent polynomials associated with a strong distribution with respect to a parameter is discussed. A natural analog of a classical result of A. Markov is proved. Recent results of Ismail and Muldoon based on the Hellman-Feynman theorem are also extended to a monotonicity criterion for zeros of Laurent polynomials. Results concerning the behaviour of extreme ...
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We consider interlacing properties satisfied by the zeros of Jacobi polynomials in quasi-orthogonal sequences characterised by α > −1, −2 < β < −1. We give necessary and sufficient conditions under which a conjecture by Askey, that the zeros of Jacobi polynomials P (α,β) n and P (α,β+2) n are interlacing, holds when the parameters α and β are in the range α > −1 and −2 < β < −1. We prove that t...
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We consider a problem of bounding the maximal possible multiplicity of a zero of some expansions ∑ aiFi(x), at a certain point c, depending on the chosen family {Fi}. The most important example is a polynomial with c = 1. It is shown that this question naturally leads to discrete orthogonal polynomials. Using this connection we derive some new bounds, in particular on the multiplicity of the ze...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1998
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(98)00117-4