一类带算子的矩阵元解集研究

IF 0.3 Q4 MATHEMATICS
A. Osipov
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引用次数: 5

摘要

摘要针对一类具有矩阵元素的无限三对角矩阵生成的算子,建立了其解集的二阶有限差分方程的多项式解的表征。这使我们能够描述相应的向量正交多项式系统在解集上的一些渐近行为。我们还发现由无限Jacobi矩阵生成的算子具有该类中最大的解集。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A study of resolvent set for a class of band operators with matrix elements
Abstract For operators generated by a certain class of infinite three-diagonal matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying second order finite-difference equations. This enables us to describe some asymptotic behavior of the corresponding systems of vector orthogonal polynomials on the resolvent set. We also find that the operators generated by infinite Jacobi matrices have the largest resolvent set in this class.
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
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