Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space
International Journal of Mathematics and Mathematical Sciences, 2004 A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions.
Fred Brackx +2 more
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Asymptotics of orthogonal polynomials inside the unit circle and Szegö-Padé approximants [PDF]
, 2001 11 pages, no figures.-- MSC2000 codes: 42C05, 41A21.MR#: MR1858277 (2002h:42043)Zbl#: Zbl 1009.42016We study the asymptotic behavior of orthogonal polynomials inside the unit circle for a subclass of measures that satisfy Szegö's condition.
López Lagomasino, Guillermo +5 more
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Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices [PDF]
, 2010 We apply the method of skew-orthogonal polynomials (SOP) in the complex plane to asymmetric random matrices with real elements, belonging to two different classes. Explicit integral representations valid for arbitrary weight functions are derived for the
Akemann, G +10 more
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Fourier coefficients for Laguerre–Sobolev type orthogonal polynomials [PDF]
Arab Journal of Mathematical Sciences, 2023 Purpose – In this paper, the authors take the first step in the study of constructive methods by using Sobolev polynomials. Design/methodology/approach – To do that, the authors use the connection formulas between Sobolev polynomials and classical ...
Alejandro Molano
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Orthogonal polynomials and Möbius transformations [PDF]
Computational and Applied Mathematics, 2021 Given an orthogonal polynomial sequence on the real line, another sequence of polynomials can be found by composing these polynomials with a general Möbius transformation. In this work, we study the properties of such Möbius-transformed polynomials. We show that they satisfy an orthogonality relation in given curve of the complex plane with respect to ...
Ricardo S. Vieira, Vanessa A. Botta
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Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval [PDF]
, 2014 We consider polynomials p^w_n(x) that are orthogonal with respect to the oscillatory weight w(x)=exp(iwx) on [?1,1], where w>0 is a real parameter. A first analysis of p^?_n(x) for large values of w was carried out in connection with complex Gaussian ...
Deaño Cabrera, Alfredo, Deaño, Alfredo
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Szegő polynomials: some relations to L-orthogonal and orthogonal polynomials
Journal of Computational and Applied Mathematics, 2003 The authors consider the Szegö polynomials \(S_n(z)\) with real reflection coefficients and obtain some relations to certain self-inverse orthogonal \(L\)-polynomials defined on the unit circle and corresponding symmetric orthogonal polynomials on a real line. The polynomials obtained by rotating the coefficients in the recursive relations satisfied by
Bracciali, Cleonice Fátima +2 more
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Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations [PDF]
, 2013 We investigate semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials that satisfy three-term recurrence relations.
Clarkson, Peter
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Representing by Orthogonal Polynomials for Sums of Finite Products of Fubini Polynomials
Mathematics, 2019 In the classical connection problem, it is dealt with determining the coefficients in the expansion of the product of two polynomials with regard to any given sequence of polynomials.
Dae San Kim +3 more
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RECURRENCE RELATIONS FOR SOBOLEV ORTHOGONAL POLYNOMIALS
Проблемы анализа, 2020 We consider recurrence relations for the polynomials orthonormal with respect to the Sobolev-type inner product and generated by classical orthogonal polynomials, namely: Jacobi polynomials, Legendre polynomials, Chebyshev polynomials of the first and ...
M. S. Sultanakhmedov
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