### 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 language | English (US) |
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Title of host publication | Applied Mathematical Sciences (Switzerland) |

Publisher | Springer |

Pages | 165-216 |

Number of pages | 52 |

DOIs | |

State | Published - Jan 1 2018 |

### Publication series

Name | Applied Mathematical Sciences (Switzerland) |
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Volume | 201 |

ISSN (Print) | 0066-5452 |

ISSN (Electronic) | 2196-968X |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*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

}

TY - CHAP

T1 - Spectral Theory for Linear Operators

AU - Magal, Pierre

AU - Ruan, Shigui

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85068166618&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068166618&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-01506-0_4

DO - 10.1007/978-3-030-01506-0_4

M3 - Chapter

T3 - Applied Mathematical Sciences (Switzerland)

SP - 165

EP - 216

BT - Applied Mathematical Sciences (Switzerland)

PB - Springer

ER -