Fractional Pantograph Delay Equations Solving by the Meshless Methods
Ibn Al-Haitham Journal for Pure and Applied Sciences, 2023 This work describes two efficient and useful methods for solving fractional pantograph delay equations (FPDEs) with initial and boundary conditions.
Shefaa M. N. Jasim, Ghada H. Ibraheem
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Riesz's Theorem for Orthogonal Matrix Polynomials [PDF]
Constructive Approximation, 1999 We describe the image through the Stieltjes transform of the set of solutions V of a matrix moment problem. We extend Riesz's theorem to the matrix setting, proving that those matrices of measures of V for which the matrix polynomials are dense in the corresponding L2 space are precisely those whose Stieltjes transform is an extremal point (in the ...
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Orthogonal Polynomials, Paraorthogonal Polynomials, and Point Perturbation [PDF]
, 2009 This thesis consists of three parts. Part 1 starts with an introduction to orthogonal polynomials, to be followed by some well-known theorems pertinent to the results we shall discuss.
Wong, Manwah Lilian
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2D-fractional Muntz–Legendre polynomials for solving the fractional partial differential equations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2020 We present a numerical method for solving linear and nonlinear fractional partial differential equations (FPDEs) with variable coefficients. The main aim of the proposed method is to introduce an orthogonal basis of twodimensional fractional Muntz ...
E. Hengamian Asl +2 more
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Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials
Advances in Mathematical Physics, 2018 Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived.
Oksana Bihun, Clark Mourning
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Riemannian Gaussian distributions, random matrix ensembles and diffusion kernels
Nuclear Physics B, 2021 We show that the Riemannian Gaussian distributions on symmetric spaces, introduced in recent years, are of standard random matrix type. We exploit this to compute analytically marginals of the probability density functions.
Leonardo Santilli, Miguel Tierz
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Random Block Matrices and Matrix Orthogonal Polynomials [PDF]
Journal of Theoretical Probability, 2008 In this paper we consider random block matrices, which generalize the general beta ensembles, which were recently investigated by Dumitriu and Edelmann (2002, 2005). We demonstrate that the eigenvalues of these random matrices can be uniformly approximated by roots of matrix orthogonal polynomials which were investigated independently from the random ...
Dette, Holger, Reuther, Bettina
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Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles [PDF]
, 2010 We consider a family of chiral non-Hermitian Gaussian random matrices in the unitarily invariant symmetry class. The eigenvalue distribution in this model is expressed in terms of Laguerre polynomials in the complex plane.
Akemann, G, Bender, M
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Asymptotics of orthogonal polynomials generated by a Geronimus perturbation of the Laguerre measure [PDF]
, 2016 This paper deals with monic orthogonal polynomials generated by a Geronimus canonical spectral transformation of the Laguerre classical measure for x in [0,?), ?
Deaño Cabrera, Alfredo +6 more
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Matrix orthogonal polynomials whose derivatives are also orthogonal
Journal of Approximation Theory, 2007 49 ...
María José Cantero +2 more
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