Spectral theory for nonlinear operators: Quadratic case

Yakov Krasnov

doi:10.1007/978-3-030-26748-3_12

Spectral theory for nonlinear operators: Quadratic case

Yakov Krasnov

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

In many cases, given a non-linear map, linearized systems near its fixed points do qualitatively capture its topological and algebraic properties. This suggests to extend the linear spectral theory to non-linear operators by considering spectra of linearizations in small neighborhoods of the fixed points. In the present paper, we develop this approach for quadratic maps. Several standard concepts such as asymptotic laws for splitting/gluing zeros of polynomial maps) are considered from new (and, possibly, unexpected) angles.

Original language	English
Title of host publication	Modern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Revised and Extended Contributions
Editors	Alexey Karapetyants, Vladislav Kravchenko, Elijah Liflyand
Publisher	Springer New York LLC
Pages	199-216
Number of pages	18
ISBN (Print)	9783030267476
DOIs	https://doi.org/10.1007/978-3-030-26748-3_12
State	Published - 2019
Event	International Scientific Conference of Modern Methods and Problems of Operator Theory and Harmonic Analysis and Their Applications, OTHA 2018 - Rostov-on-Don, Russian Federation Duration: 22 Apr 2018 → 27 Apr 2018

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	291
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Scientific Conference of Modern Methods and Problems of Operator Theory and Harmonic Analysis and Their Applications, OTHA 2018
Country/Territory	Russian Federation
City	Rostov-on-Don
Period	22/04/18 → 27/04/18

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2019.

Keywords

Bilinear operator
Cumulative spectrum
Nonlinear spectral theory

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10.1007/978-3-030-26748-3_12

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Krasnov, Y. (2019). Spectral theory for nonlinear operators: Quadratic case. In A. Karapetyants, V. Kravchenko, & E. Liflyand (Eds.), Modern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Revised and Extended Contributions (pp. 199-216). (Springer Proceedings in Mathematics and Statistics; Vol. 291). Springer New York LLC. https://doi.org/10.1007/978-3-030-26748-3_12

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abstract = "In many cases, given a non-linear map, linearized systems near its fixed points do qualitatively capture its topological and algebraic properties. This suggests to extend the linear spectral theory to non-linear operators by considering spectra of linearizations in small neighborhoods of the fixed points. In the present paper, we develop this approach for quadratic maps. Several standard concepts such as asymptotic laws for splitting/gluing zeros of polynomial maps) are considered from new (and, possibly, unexpected) angles.",

keywords = "Bilinear operator, Cumulative spectrum, Nonlinear spectral theory",

author = "Yakov Krasnov",

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Krasnov, Y 2019, Spectral theory for nonlinear operators: Quadratic case. in A Karapetyants, V Kravchenko & E Liflyand (eds), Modern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Revised and Extended Contributions. Springer Proceedings in Mathematics and Statistics, vol. 291, Springer New York LLC, pp. 199-216, International Scientific Conference of Modern Methods and Problems of Operator Theory and Harmonic Analysis and Their Applications, OTHA 2018, Rostov-on-Don, Russian Federation, 22/04/18. https://doi.org/10.1007/978-3-030-26748-3_12

Spectral theory for nonlinear operators: Quadratic case. / Krasnov, Yakov.
Modern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Revised and Extended Contributions. ed. / Alexey Karapetyants; Vladislav Kravchenko; Elijah Liflyand. Springer New York LLC, 2019. p. 199-216 (Springer Proceedings in Mathematics and Statistics; Vol. 291).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Spectral theory for nonlinear operators: Quadratic case

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