Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle
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Publication:868788
DOI10.1016/j.jmaa.2006.06.076zbMath1110.33004arXivmath/0606037OpenAlexW2008158889MaRDI QIDQ868788
Publication date: 26 February 2007
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0606037
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)
Related Items (29)
Markov's theorem for weight functions on the unit circle ⋮ Large deviations for spectral measures of some spiked matrices ⋮ First and second kind paraorthogonal polynomials and their zeros ⋮ \(R_{II}\) type recurrence, generalized eigenvalue problem and orthogonal polynomials on the unit circle ⋮ Twelve tales in mathematical physics: An expanded Heineman prize lecture ⋮ Refined interlacing properties for zeros of paraorthogonal polynomials on the unit circle ⋮ Zero spacings of paraorthogonal polynomials on the unit circle ⋮ Poncelet's theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators ⋮ A generalized eigenvalue problem for quasi-orthogonal rational functions ⋮ On the spacing of zeros of paraorthogonal polynomials for singular measures ⋮ On bi-orthogonal systems of trigonometric functions and quadrature formulas for periodic integrands ⋮ Zeros of non-Baxter paraorthogonal polynomials on the unit circle ⋮ Monotonicity of zeros for a class of polynomials including hypergeometric polynomials ⋮ On the existence of para-orthogonal rational functions on the unit circle ⋮ Two extensions of Lubinsky's universality theorem ⋮ Positive trigonometric quadrature formulas and quadrature on the unit circle ⋮ Inverse spectral problems for a class of pentadiagonal unitary matrices ⋮ Para-orthogonal polynomials from constant Verblunsky coefficients ⋮ Szegő-type quadrature formulas ⋮ On monotonicity of zeros of paraorthogonal polynomials on the unit circle ⋮ On a class of extremal solutions of the nondegenerate matricial Carathéodory problem ⋮ Weak convergence of CD kernels and applications ⋮ Perturbations of Jordan matrices ⋮ An Electrostatic Interpretation of the Zeros of Paraorthogonal Polynomials on the Unit Circle ⋮ Poisson brackets of orthogonal polynomials ⋮ Zeros of quasi-paraorthogonal polynomials and positive quadrature ⋮ Some spectral applications of McMullen’s Hausdorff dimension algorithm ⋮ A connection between Szegő-Lobatto and quasi Gauss-type quadrature formulas ⋮ Zeros of para-orthogonal polynomials and linear spectral transformations on the unit circle
Cites Work
- Quadrature formula and zeros of para-orthogonal polynomials on the unit circle
- Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle
- Measures on the unit circle and unitary truncations of unitary operators
- CMV matrices: Five years after
- Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle
- OPUC on one foot
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