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Orthogonal polynomials and Mobius transformations
(Springer, 2021-09-01)
Given an orthogonal polynomial sequence on the real line, another sequence of polynomials can be found by composing them with a Mobius transformation. In this work, we study the properties of such Mobius-transformed ...
Kernel polynomials from L-orthogonal polynomials
(2011-05-01)
A positive measure ψ defined on [a,b] such that its moments μn=∫a btndψ(t) exist for n=0,±1,±2,⋯, is called a strong positive measure on [a,b]. If 0≤a<b≤∞ then the sequence of (monic) polynomials {Qn}, defined by ∫a ...
Interlacing of zeros of orthogonal polynomials under modification of the measure
(2013-11-01)
We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure dμ (x), supported on the interval (a, b) and the other with respect ...
Multivariate sobolev-type orthogonal polynomials
(2011-12-01)
Multivariate orthogonal polynomials associated with a Sobolev-type inner product, that is, an inner product defined by adding to a measure the evaluation of the gradients in a fixed point, are studied. Orthogonal polynomials ...
Another connection between orthogonal polynomials and L-orthogonal polynomials
(Elsevier B.V., 2007-06-01)
We consider a connection that exists between orthogonal polynomials associated with positive measures on the real line and orthogonal Laurent polynomials associated with strong measures of the class S-3 [0, beta, b]. ...
Zeros of Jacobi-Sobolev orthogonal polynomials following non-coherent pair of measures
(2010-12-14)
Zeros of orthogonal polynomials associated with two different Sobolev inner products involving the Jacobi measure are studied. In particular, each of these Sobolev inner products involves a pair of closely related Jacobi ...
Zeros of classical orthogonal polynomials of a discrete variable
(Amer Mathematical Soc, 2013-04-01)
In this paper we obtain sharp bounds for the zeros of classical orthogonal polynomials of a discrete variable, considered as functions of a parameter, by using a theorem of A. Markov and the so-called Hellmann-Feynman ...
Real orthogonal polynomials in frequency analysis
(Amer Mathematical Soc, 2004-01-01)
We study the use of para-orthogonal polynomials in solving the frequency analysis problem. Through a transformation of Delsarte and Genin, we present an approach for the frequency analysis by using the zeros and Christoffel ...
Inequalities for zeros of associated polynomials and derivatives of orthogonal polynomials
(Elsevier B.V., 2001-02-01)
It is well known and easy to see that the zeros of both the associated polynomial and the derivative of an orthogonal polynomial p(n)(x) interlace with the zeros of p(n)(x) itself. The natural question of how these zeros ...
SYMMETRICAL ORTHOGONAL POLYNOMIALS AND THE ASSOCIATED ORTHOGONAL L-POLYNOMIALS
(Amer Mathematical Soc, 1995-10-01)
We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained Finally as an application, we derive ...