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On the spectrum of difference relations and differential operators in weighted spaces of sequences and functions


Author: S. B. Besaeva
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 26 (2014), nomer 4.
Journal: St. Petersburg Math. J. 26 (2015), 499-513
MSC (2010): Primary 47A06
Published electronically: May 6, 2015
MathSciNet review: 3289184
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Abstract | References | Similar Articles | Additional Information

Abstract: Spectral properties are described for difference relations defined in weighted spaces of sequences of vectors. All conceivable conditions imposed on the weight are taken into account. In the proofs, a similarity transformation is employed to reshape the relation in question to another relation in a nonweighted space. The results are applied to the spectrum description for a differential operator acting in a weighted space of measurable functions.


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Additional Information

S. B. Besaeva
Affiliation: Mathematics Department, K. L. Khetagurov North Osetia state university, Vatutin str. 46, Vladikavkaz 362025, Russia
Email: besaevasv@mail.ru

DOI: https://doi.org/10.1090/spmj/1349
Keywords: Linear relation, spectrum of a linear difference ratio, spectrum of a differential operator, resolvent, similarity transformation
Received by editor(s): May 7, 2013
Published electronically: May 6, 2015
Additional Notes: Supported by RFBR (grant no. 10-01-00276)
Article copyright: © Copyright 2015 American Mathematical Society