The Inverse Spectral Problem for Jacobi-Type Pencils
Copyright policy )The Inverse Spectral Problem for Jacobi-Type Pencils
In this paper we study the inverse spectral problem for Jacobi-type pencils. By a Jacobi-type pencil we mean the following pencil $J_5 - λJ_3$, where $J_3$ is a Jacobi matrix and $J_5$ is a semi-infinite real symmetric five-diagonal matrix with positive numbers on the second subdiagonal. In the case of a special perturbation of orthogonal polynomials on a finite interval the corresponding spectral function takes an explicit form.
operator pencil, 42C05, Mathematics - Classical Analysis and ODEs, Jacobi (tridiagonal) operators (matrices) and generalizations, recurrence relation, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Jacobi-type pencils, spectral function, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, orthogonal polynomials
operator pencil, 42C05, Mathematics - Classical Analysis and ODEs, Jacobi (tridiagonal) operators (matrices) and generalizations, recurrence relation, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Jacobi-type pencils, spectral function, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, orthogonal polynomials
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