Spectral Theory for Linear Operators

Pierre Magal, Shigui Ruan

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter covers fundamental results on the spectral theory, including Fredholm alternative theorem and Nussbaum’s theorem on the radius of essential spectrum for bounded linear operators; growth bound and essential growth bound of linear operators; the relationship between the spectrum of semigroups and the spectrum of their infinitesimal generators; spectral decomposition of the state space; and asynchronous exponential growth of linear operators. The estimates of growth bound and essential growth bound of linear operators will be used in proving the center manifold theorem in Chapter 6.

Original languageEnglish (US)
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages165-216
Number of pages52
DOIs
StatePublished - Jan 1 2018

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume201
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Fingerprint

Spectral Theory
Linear Operator
Fredholm Alternative
Alternative Theorems
Center Manifold Theorem
Spectral Decomposition
Infinitesimal Generator
Essential Spectrum
Exponential Growth
Bounded Linear Operator
State Space
Semigroup
Radius
Cover
Decomposition
Theorem
Estimate

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Magal, P., & Ruan, S. (2018). Spectral Theory for Linear Operators. In Applied Mathematical Sciences (Switzerland) (pp. 165-216). (Applied Mathematical Sciences (Switzerland); Vol. 201). Springer. https://doi.org/10.1007/978-3-030-01506-0_4

Spectral Theory for Linear Operators. / Magal, Pierre; Ruan, Shigui.

Applied Mathematical Sciences (Switzerland). Springer, 2018. p. 165-216 (Applied Mathematical Sciences (Switzerland); Vol. 201).

Research output: Chapter in Book/Report/Conference proceedingChapter

Magal, P & Ruan, S 2018, Spectral Theory for Linear Operators. in Applied Mathematical Sciences (Switzerland). Applied Mathematical Sciences (Switzerland), vol. 201, Springer, pp. 165-216. https://doi.org/10.1007/978-3-030-01506-0_4
Magal P, Ruan S. Spectral Theory for Linear Operators. In Applied Mathematical Sciences (Switzerland). Springer. 2018. p. 165-216. (Applied Mathematical Sciences (Switzerland)). https://doi.org/10.1007/978-3-030-01506-0_4
Magal, Pierre ; Ruan, Shigui. / Spectral Theory for Linear Operators. Applied Mathematical Sciences (Switzerland). Springer, 2018. pp. 165-216 (Applied Mathematical Sciences (Switzerland)).
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