Results 11 to 20 of about 984,401 (366)
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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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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On Sobolev orthogonal polynomials [PDF]
Expositiones Mathematicae, 2015 Sobolev orthogonal polynomials have been studied extensively in the past 20 years. The research in this field has sprawled into several directions and generates a plethora of publications. This paper contains a survey of the main developments up to now.
Francisco Marcellán, Yuan Xu
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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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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
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Fourier Transform of the Orthogonal Polynomials on the Unit Ball and Continuous Hahn Polynomials
Axioms, 2022 Some systems of univariate orthogonal polynomials can be mapped into other families by the Fourier transform. The most-studied example is related to the Hermite functions, which are eigenfunctions of the Fourier transform.
Esra Güldoğan Lekesiz +2 more
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A Note on Bi-Orthogonal Polynomials and Functions
Fluids, 2020 The theory of orthogonal polynomials is well established and detailed, covering a wide field of interesting results, as, in particular, for solving certain differential equations.
Clemente Cesarano
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Free-Fermion entanglement and orthogonal polynomials [PDF]
Journal of Statistical Mechanics: Theory and Experiment, 2019 We present a simple construction for a tridiagonal matrix T that commutes with the hopping matrix for the entanglement Hamiltonian of open finite free-Fermion chains associated with families of discrete orthogonal polynomials.
N. Crampé +2 more
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Generalizations of orthogonal polynomials [PDF]
Journal of Computational and Applied Mathematics, 2005 The paper is a clearly written survey. The following generalizations of orthogonal polynomials are considered: orthogonal rational functions; homogeneous multivariate orthogonal polynomials; vector and matrix orthogonal polynomials; multiple orthogonal polynomials.
Bultheel, Adhemar +4 more
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On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle
Mathematics, 2020 In this contribution, we propose an algorithm to compute holonomic second-order differential equations satisfied by some families of orthogonal polynomials.
Lino G. Garza +2 more
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