The similarity problem for non-selfadjoint operators with absolutely continuous spectrum: Restrictions to spectral subspaces

Alexander V. Kiselev

doi:10.1007/978-3-7643-9994-8_5

The similarity problem for non-selfadjoint operators with absolutely continuous spectrum: Restrictions to spectral subspaces

Alexander V. Kiselev

Department of Mathematical Sciences

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

3 Citations (SciVal)

Abstract

The similarity problem for restrictions of a non-selfadjoint operator with absolutely continuous spectrum to its spectral subspaces corresponding to arbitrary Borel subsets δ of the spectrum is considered, generalizing the results of [7, 11]. Necessary and sufficient conditions of such similarity are obtained in the form of a pair of integral estimates on δ ⊂ ℝ. The results are then applied to the analysis of the one-dimensional non-selfadjoint Friedrichs model operator.

Original language	English
Title of host publication	Spectral Theory and Analysis - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2008
Editors	Jan Janas, Pavel Kurasov, Ari Laptev, Ari Laptev, Sergei Naboko, Günter Stolz
Publisher	Springer International Publishing
Pages	67-82
Number of pages	16
ISBN (Print)	9783764399931
DOIs	https://doi.org/10.1007/978-3-7643-9994-8_5
Publication status	Published - 2011
Event	Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2008 - Bedlewo, Poland Duration: 1 Jan 2008 → …

Publication series

Name	Operator Theory: Advances and Applications
Volume	214
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

Conference

Conference	Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2008
Country/Territory	Poland
City	Bedlewo
Period	1/01/08 → …

Keywords

Absolutely continuous spectrum
Non-selfadjoint operators
Similarity problem

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/978-3-7643-9994-8_5

Cite this

Kiselev, A. V. (2011). The similarity problem for non-selfadjoint operators with absolutely continuous spectrum: Restrictions to spectral subspaces. In J. Janas, P. Kurasov, A. Laptev, A. Laptev, S. Naboko, & G. Stolz (Eds.), Spectral Theory and Analysis - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2008 (pp. 67-82). (Operator Theory: Advances and Applications; Vol. 214). Springer International Publishing. https://doi.org/10.1007/978-3-7643-9994-8_5

The similarity problem for non-selfadjoint operators with absolutely continuous spectrum: Restrictions to spectral subspaces. / Kiselev, Alexander V.
Spectral Theory and Analysis - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2008. ed. / Jan Janas; Pavel Kurasov; Ari Laptev; Ari Laptev; Sergei Naboko; Günter Stolz. Springer International Publishing, 2011. p. 67-82 (Operator Theory: Advances and Applications; Vol. 214).

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Kiselev, AV 2011, The similarity problem for non-selfadjoint operators with absolutely continuous spectrum: Restrictions to spectral subspaces. in J Janas, P Kurasov, A Laptev, A Laptev, S Naboko & G Stolz (eds), Spectral Theory and Analysis - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2008. Operator Theory: Advances and Applications, vol. 214, Springer International Publishing, pp. 67-82, Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2008, Bedlewo, Poland, 1/01/08. https://doi.org/10.1007/978-3-7643-9994-8_5

Kiselev AV. The similarity problem for non-selfadjoint operators with absolutely continuous spectrum: Restrictions to spectral subspaces. In Janas J, Kurasov P, Laptev A, Laptev A, Naboko S, Stolz G, editors, Spectral Theory and Analysis - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2008. Springer International Publishing. 2011. p. 67-82. (Operator Theory: Advances and Applications). doi: 10.1007/978-3-7643-9994-8_5

Kiselev, Alexander V. / The similarity problem for non-selfadjoint operators with absolutely continuous spectrum : Restrictions to spectral subspaces. Spectral Theory and Analysis - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2008. editor / Jan Janas ; Pavel Kurasov ; Ari Laptev ; Ari Laptev ; Sergei Naboko ; Günter Stolz. Springer International Publishing, 2011. pp. 67-82 (Operator Theory: Advances and Applications).

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The similarity problem for non-selfadjoint operators with absolutely continuous spectrum: Restrictions to spectral subspaces

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