Matrix polynomials orthogonal with respect to a non-symmetric matrix of measures

• Autorzy: Zygmunt M. J.

Identyfikatory

DOI

10.7494/OpMath.2016.36.3.409

• Języki publikacji: EN

Abstrakty

EN

The paper focuses on matrix-valued polynomials satisfying a three-term recurrence relation with constant matrix coefficients. It is shown that they form an orthogonal system with respect to a matrix of measures, not necessarily symmetric. Moreover, it is stated the condition on the coefficients of the recurrence formula for which the matrix measure is symmetric.

Słowa kluczowe

EN

matrix orthogonal polynomials; recurrence formula; matrix of measures; block Jacobi matrices

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 3
• Strony: 409--423
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Zygmunt M. J.

• AGH University of Science and Technology Faculty of Applied Mathematics al. A. Mickiewicza 30, 30-059 Krakow, Poland

Bibliografia

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• [8] F.A. Grunbaum, M.D. de la Iglesia, Matrix valued orthogonal polynomials arising from group representation theory and a family of quasi-birth-and-death processes, SIAM J. Matrix Anal. Applic. 30 (2008) 2, 741-761.
• [9] M.G. Krein, Infinite J -matrices and a matrix moment problem, Doki. Akad. Nauk SSSR 69 (1949), 125-128 [in Russian].
• [10] M.A. Naimark, Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint operator of second order on a semi-axis, Trudy Mosk. Mat. Obs. 3 (1954), 181-270 [in Russian].
• [II] A. Sinap, W. Van Assche, Orthogonal matrix polynomials and applications, J. Comput. Appl. Math. 66 (1996), 27-52.
• [12] G. Szego, Orthogonal Polynomials, AMS Coll. Pub., vol. 23, AMS, Providence, 1975 (4th edition).
• [13] M.J. Zygmunt, Matrix orthogonal polynomials and continued fractions, Linear Alg. Appl. 340, (2002) 1-3, 155-168.
• [14] M.J. Zygmunt, Jacobi block matrices with constant matrix terms, Oper. Th.: Adv. & Appl. 154 (2004), 233-238.
• [15] M.J. Zygmunt, Non symmetric random walk on infinite graph, Opuscula Math. 31, (2011) 4, 669-674.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.