Complex Jacobi matrices and quadrature rules
نویسندگان
چکیده
منابع مشابه
Complex Jacobi Matrices
Complex Jacobi matrices play an important role in the study of asymptotics and zero distribution of Formal Orthogonal Polynomials (FOPs). The latter are essential tools in several elds of Numerical Analysis, for instance in the context of iterative methods for solving large systems of linear equations, or in the study of Pad e approximation and Jacobi continued fractions. In this paper we prese...
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Let Ej be the eigenvalues outside [−2, 2] of a Jacobi matrix with an − 1 ∈ ` and bn → 0, and μ′ the density of the a.c. part of the spectral measure for the vector δ1. We show that if bn / ∈ `, bn+1 − bn ∈ `, then ∑ j (|Ej | − 2) = ∞, and if bn ∈ `, bn+1 − bn / ∈ `, then ∫ 2 −2 ln(μ′(x))(4− x) dx = −∞. We also show that if an − 1, bn ∈ `, then the above integral is finite if and only if an+1 − ...
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ژورنال
عنوان ژورنال: Filomat
سال: 2003
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil0317117m