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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access May 17, 2016

A study of resolvent set for a class of band operators with matrix elements

Andrey Osipov
From the journal Concrete Operators

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.

References

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Received: 2015-12-9
Accepted: 2016-5-3
Published Online: 2016-5-17

© 2016 Andrey Osipov

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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