Orthogonal polynomials on ellipses and their recurrence relations

• Autorzy: Lauric V.
• Języki publikacji: EN

Abstrakty

EN

In this note we study the connection between orthogonal polynomials on an ellipse and orthogonal Laurent polynomials on the unit circle relative to some multiplicative measures and then establish the recurrence relations for orthogonal polynomials on an ellipse. The matrix representation of the operator of multiplication by coordinate function is obtained.

Słowa kluczowe

EN

orthogonal polynomials on ellipses; recurrence relation; Hessenberg matrix

PL

wielomiany ortogonalne; macierz Hessenberga

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 1
• Strony: 137--145
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Lauric V.

• Department of Mathematics, Florida A&M University, Tallahassee, FL 32307, U.S.A.

Bibliografia

• [1] M. Cantero, L. Moral, L. Velazquez, Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle, Linear Algebra Appl. 362 (2003), 29–56.
• [2] A. Dovgoshei, Three-term recurrence relation for polynomials orthogonal with respect to harmonic measure, Ukrainian Math. J. 53(2) (2001), 167–177.
• [3] P. Duren, Extension of a result of Beurling on invariant subspaces, Trans. Amer. Math. Soc. 99 (1961), 320–324.
• [4] P. Duren, Invariant subspaces of tridiagonal operators, Duke Math. J. 30 (1963), 239–248.
• [5] P. Duren, Polynomials orthogonal over a curve, Michigan Math. J. 12(3) (1965), 313–316.
• [6] D. Khavinson, N. Stylianopoulos, Recurrence relations for orthogonal polynomials and algebraicity of solutions of the Dirichlet problem, International Mathematical Series 12 (2010), 219–228.
• [7] M. Putinar, N. Stylianopoulos, Finite-term relations for planar orthogonal polynomials, Aompl. Anal. Oper. Theory 1 (2007), 447–456.
• [8] B. Simon, Orthogonal Polynomial on the Unit Circle, Part 1: Classical Theory, AMS Colloquium Publications, American Mathematical Society, Providence, RI 54 (2005).
• [9] B. Simon, Orthogonal Polynomial on the Unit Circle, Part 2: Spectral Theory, AMS Colloquium Publications, American Mathematical Society, Providence, RI 54 (2005).
• [10] L. Velazquez, Spectral methods for orthogonal rational functions, J. Functional Analysis 254(4) (2003), 954–986.