Results 101 to 110 of about 411,141 (342)
A Unified Approach to Computing the Zeros of Orthogonal Polynomials
Journal of New Theory, 2023 We present a unified approach to calculating the zeros of the classical orthogonal polynomials and discuss the electrostatic interpretation and its connection to the energy minimization problem. This approach works for the generalized Bessel polynomials,
Ridha Moussa, James Tipton
doaj +1 more source
No‐regret and low‐regret control for a weakly coupled abstract hyperbolic system
Asian Journal of Control, EarlyView.Abstract This paper explores an optimal control problem of weakly coupled abstract hyperbolic systems with missing initial data. Hyperbolic systems, known for their wave‐like phenomena and complexity, become even more challenging with weak coupling between subsystems.
Meriem Louafi +3 more
wiley +1 more source
Complex versus real orthogonal polynomials of two variables [PDF]
arXiv, 2013 Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex Hermite orthogonal polynomials and the disk polynomials are used as illustrating examples.
arxiv
Equilibria of `Discrete' Integrable Systems and Deformations of Classical Orthogonal Polynomials
, 2004 The Ruijsenaars-Schneider systems are `discrete' version of the Calogero-Moser (C-M) systems in the sense that the momentum operator p appears in the Hamiltonians as a polynomial in e^{\pm\beta' p} (\beta' is a deformation parameter) instead of an ...
Andrews G E +29 more
core +3 more sources
Analysis of density matrix embedding theory around the non‐interacting limit
Communications on Pure and Applied Mathematics, EarlyView.Abstract This article provides the first mathematical analysis of the Density Matrix Embedding Theory (DMET) method. We prove that, under certain assumptions, (i) the exact ground‐state density matrix is a fixed‐point of the DMET map for non‐interacting systems, (ii) there exists a unique physical solution in the weakly‐interacting regime, and (iii ...
Eric Cancès +4 more
wiley +1 more source
Orthogonal polynomials related to the unit circle and differential-difference equations [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1997 In this paper we obtain the orthogonal polynomial sequences, related to the unit circle, that verify the following differential-difference equation: (z − α)(z − β)φ'_n(z)/n = (z + αn)φ_n(z) + β_nφ_{n−1}(z) .
A. Cachafeiro, C. Suárez
doaj
A characterization of the four Chebyshev orthogonal families
International Journal of Mathematics and Mathematical Sciences, 2005 We obtain a property which characterizes the Chebyshev orthogonal polynomials of first, second, third, and fourth kind. Indeed, we prove that the four Chebyshev sequences are the unique classical orthogonal polynomial families such that their linear ...
E. Berriochoa +2 more
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Communications on Pure and Applied Mathematics, EarlyView.Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
wiley +1 more source
Tridiagonal Operators and Zeros of Polynomials in Two Variables
Abstract and Applied Analysis, 2016 The aim of this paper is to connect the zeros of polynomials in two variables with the eigenvalues of a self-adjoint operator. This is done by use of a functional-analytic method.
Chrysi G. Kokologiannaki +2 more
doaj +1 more source
Surveys in Approximation Theory, 1 (2005), 70-125, 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.
arxiv