On the spectrum of difference relations and differential operators in weighted spaces of sequences and functions
HTML articles powered by AMS MathViewer
- by
S. B. Besaeva
Translated by: A. Plotkin - St. Petersburg Math. J. 26 (2015), 499-513
- DOI: https://doi.org/10.1090/spmj/1349
- Published electronically: May 6, 2015
- PDF | Request permission
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
- 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, DOI 10.1070/SM2002v193n11ABEH000696
- 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, DOI 10.1070/IM2009v073n02ABEH002445
- 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, DOI 10.1007/s10958-006-0286-4
- 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, DOI 10.1070/rm2013v068n01abeh004822
- 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, DOI 10.3103/S1066369X11020022
- 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)
- Nelson Dunford and Jacob T. Schwartz, Linear operators. Part III: Spectral operators, Pure and Applied Mathematics, Vol. VII, Interscience Publishers [John Wiley & Sons], New York-London-Sydney, 1971. With the assistance of William G. Bade and Robert G. Bartle. MR 0412888
Bibliographic Information
- S. B. Besaeva
- Affiliation: Mathematics Department, K. L. Khetagurov North Osetia state university, Vatutin str. 46, Vladikavkaz 362025, Russia
- Email: besaevasv@mail.ru
- Received by editor(s): May 7, 2013
- Published electronically: May 6, 2015
- Additional Notes: Supported by RFBR (grant no. 10-01-00276)
- © Copyright 2015 American Mathematical Society
- Journal: St. Petersburg Math. J. 26 (2015), 499-513
- MSC (2010): Primary 47A06
- DOI: https://doi.org/10.1090/spmj/1349
- MathSciNet review: 3289184