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Krylov complexity and orthogonal polynomials [PDF]
Nuclear Physics B, 2022 Krylov complexity measures operator growth with respect to a basis, which is adapted to the Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm, also known as the recursion method.
Wolfgang Mück, Yi Yang
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NIST Handbook of Mathematical Functions, 2005 In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.
T. Koornwinder +3 more
semanticscholar +6 more sources
Constrained Orthogonal Polynomials [PDF]
Journal of Physics A: Mathematical and General, 2005 We define sets of orthogonal polynomials satisfying the additional constraint of a vanishing average. These are of interest, for example, for the study of the Hohenberg-Kohn functional for electronic or nucleonic densities and for the study of density ...
B G Giraud +3 more
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Planar orthogonal polynomials as Type II multiple orthogonal polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2019 We show that the planar orthogonal polynomials with $l$ logarithmic singularities in the potential are the multiple orthogonal polynomials (Hermite-Pad polynomials) of Type II with $l$ measures. We also find the ratio between the determinant of the moment matrix corresponding to the multiple orthogonal polynomials and the determinant of the moment ...
Seung-Yeop Lee, Meng Yang
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Coherent Orthogonal Polynomials [PDF]
Annals of Physics, 2012 We discuss as a fundamental characteristic of orthogonal polynomials like the existence of a Lie algebra behind them, can be added to their other relevant aspects.
Cambanis +9 more
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A conjecture on Exceptional Orthogonal Polynomials [PDF]
Foundations of Computational Mathematics, 2012 Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials.
A. González-López +42 more
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Multiple orthogonal polynomials: Pearson equations and Christoffel formulas [PDF]
Analysis and Mathematical Physics, 2021 Multiple orthogonal polynomials with respect to two weights on the step-line are considered. A connection between different dual spectral matrices, one banded (recursion matrix) and one Hessenberg, respectively, and the Gauss–Borel factorization of the ...
A. Branquinho +2 more
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Multiple orthogonal polynomials with respect to Gauss' hypergeometric function [PDF]
Studies in applied mathematics (Cambridge), 2020 A new set of multiple orthogonal polynomials of both type I and type II with respect to two weight functions involving Gauss' hypergeometric function on the interval (0,1) is studied.
Hélder Lima, A. Loureiro
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Some New Families of Finite Orthogonal Polynomials in Two Variables
Axioms, 2023 In this paper, we generalize the study of finite sequences of orthogonal polynomials from one to two variables. In doing so, twenty three new classes of bivariate finite orthogonal polynomials are presented, obtained from the product of a finite and an ...
Esra Güldoğan Lekesiz, Iván Area
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Complexity, 2022 In this contribution, we use the connection between stable polynomials and orthogonal polynomials on the real line to construct sequences of Hurwitz polynomials that are robustly stable in terms of several uncertain parameters.
Alejandro Arceo +4 more
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