Results 11 to 20 of about 5,897 (225)
Matrix valued Jacobi polynomials [PDF]
Bulletin des Sciences Mathématiques, 2003 The author finds a matrix valued weight for Jacobi orthogonal polynomials, which satisfy an explicit differential equation of Jabobi type. An application to spherical functions is discussed. The Bochner problem of finding all families of orthogonal polynomials that are eigenfunctions of some second order differential operator is considered.
Grünbaum, F.Alberto
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Upward Extension of the Jacobi Matrix for Orthogonal Polynomials [PDF]
Journal of Approximation Theory, 1996 Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We investigate new orthogonal polynomials by adding to the Jacobi matrix $r$ new rows and columns, so that the original
Ronveaux, André, Van Assche, Walter
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The study of Jacobi and cyclic Jacobi matrix eigenvalue problems using Sturm–Liouville theory [PDF]
Linear Algebra and its Applications, 2011 \textit{Q. Kong} et al. [J. Math. Anal. Appl. 263, No. 2, 748--762 (2001; Zbl 1001.34019)] discovered a class of Sturm-Liouville problems (SLPs) whose spectrum is a finite set of eigenvalues and earlier in [Result. Math. 54, No. 1-2, 103--116 (2009; Zbl 1185.34032)], the authors and \textit{H. Volkmer} obtained matrix representations of these problems.
Kong, Qingkai, Zettl, Anton
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The Spectrum of a Periodic Complex Jacobi Matrix Revisited [PDF]
Journal of Approximation Theory, 2000 Let \(G\) be a complex periodic Jacobi matrix of period \(k\), i.e. \[ G=\begin{pmatrix} b^{(0)}&a^{(1)}&0&\cdots\\ a^{(1)}&b^{(1)}&a^{(2)}&\cdots\\ 0&a^{(2)}&b^{(2)}&\cdots\\ \vdots&\vdots&\vdots&\ddots\end{pmatrix}, \] where \(a^{(n)}=a^{(j)}\), \(b^{(n)}=b^{(j)}\) for \(n\equiv j\pmod k\). This matrix defines a bounded linear operator on \(\ell^2\).
Vázquez, A.Almendral
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Space versus energy oscillations of Prufer phases for matrix Sturm-Liouville and Jacobi operators [PDF]
Electronic Journal of Differential Equations, 2020 This note considers Sturm oscillation theory for regular matrix Sturm-Liouville operators on finite intervals and for matrix Jacobi operators. The number of space oscillations of the eigenvalues of the matrix Prufer phases at a given energy, defined ...
Hermann Schulz-Baldes, Liam Urban
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Bisymmetric nonnegative Jacobi matrix realizations [PDF]
, 2023 Producción CientíficaWithin the symmetric inverse eigenvalue problem, the case of bisym- metric Jacobi matrices occupies a central place, since for any strictly monotone list of n real numbers there exists a unique bisymmetric Jacobi matrix realizing ...
Jiménez, María José +4 more
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Eigenvalues of Jacobi matrix in evolutionary game. [PDF]
, 2023 Eigenvalues of Jacobi matrix in evolutionary game.
Xiangxiao Gao (16748595) +3 more
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Integration of the finite complex Toda lattice with a self-consistent source
Partial Differential Equations in Applied Mathematics, 2023 In the paper, we derive a finite complex Toda lattice with a self-consistent source. We discuss the complete integrability of the constructed systems that is based on the transformation to the spectral data of an associated finite Jacobi matrix.
B.A. Babajanov +2 more
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Deficiency Indices of Block Jacobi Matrices: Survey
Современная математика: Фундаментальные направления, 2021 The paper is a survey and concerns with infinite symmetric block Jacobi matrices J with m×m-matrix entries. We discuss several results on general block Jacobi matrices to be either self-adjoint or have maximal as well as intermediate deficiency indices ...
Viktoriya S. Budyka +2 more
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Computing the Hessenberg matrix associated with a self-similar measure [PDF]
, 2011 We introduce in this paper a method to calculate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G.
Torrano, E. +7 more
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