Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



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
Full-text PDF

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.

References [Enhancements On Off] (What's this?)

  • 1. A. G. Baskakov and K. I. Chernyshov, Spectral analysis of linear relations, and degenerate semigroups of operators, Mat. Sb. 193 (2002), no. 11, 3–42 (Russian, with Russian summary); English transl., Sb. Math. 193 (2002), no. 11-12, 1573–1610. MR 1937028,
  • 2. A. G. Baskakov, Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations, and semigroups of difference relations, Izv. Ross. Akad. Nauk Ser. Mat. 73 (2009), no. 2, 3–68 (Russian, with Russian summary); English transl., Izv. Math. 73 (2009), no. 2, 215–278. MR 2531885,
  • 3. A. G. Baskakov, Theory of representations of Banach algebras, and abelian groups and semigroups in the spectral analysis of linear operators, Sovrem. Mat. Fundam. Napravl. 9 (2004), 3–151 (Russian); English transl., J. Math. Sci. (N.Y.) 137 (2006), no. 4, 4885–5036. MR 2123307,
  • 4. A. G. Baskakov, Investigation of linear differential equations by the methods of the spectral theory of difference operators and linear relations, Uspekhi Mat. Nauk 68 (2013), no. 1(409), 77–128 (Russian, with Russian summary); English transl., Russian Math. Surveys 68 (2013), no. 1, 69–116. MR 3088079
  • 5. M. S. Bichegkuev and S. V. Besaeva, On the spectral properties of difference and differential operators in weighted spaces, Izv. Vyssh. Uchebn. Zaved. Mat. 2 (2011), 16–21 (Russian, with English and Russian summaries); English transl., Russian Math. (Iz. VUZ) 55 (2011), no. 2, 13–17. MR 2814817,
  • 6. S. V. Besaeva, On the spectral properties of difference operators in weighted spaces, Vestnik Voronez. Gos. Univ. Ser. Fiz. Mat. 2011, no. 1, 94-99. (Russian)
  • 7. Nelson Dunford and Jacob T. Schwartz, Linear operators. Part III: Spectral operators, Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney, 1971. With the assistance of William G. Bade and Robert G. Bartle; Pure and Applied Mathematics, Vol. VII. MR 0412888

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 47A06

Retrieve articles in all journals with MSC (2010): 47A06

Additional Information

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

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

American Mathematical Society