Spectral Theory and its Applications

Bernard Helffer

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English

Cambridge University Press
17 January 2013

Mathematics & Sciences; Differential calculus & equations; Integral calculus & equations; Fluid mechanics; Mathematical physics

Series: Cambridge Studies in Advanced Mathematics

Bernard Helffer's graduate-level introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schrödinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The later chapters also introduce non self-adjoint operator theory with an emphasis on the role of the pseudospectra. The author's focus on applications, along with exercises and examples, enables readers to connect theory with practice so that they develop a good understanding of how the abstract spectral theory can be applied. The final chapter provides various problems that have been the subject of active research in recent years and will challenge the reader's understanding of the material covered.

By: Bernard Helffer
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 139
Dimensions: Height: 231mm, Width: 152mm, Spine: 18mm
Weight: 450g
ISBN: 9781107032309
ISBN 10: 110703230X
Series: Cambridge Studies in Advanced Mathematics
Pages: 260
Publication Date: 17 January 2013
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

1. Introduction; 2. Unbounded operators; 3. Representation theorems; 4. Semibounded operators; 5. Compact operators; 6. Spectral theory for bounded operators; 7. Applications in physics and PDE; 8. Spectrum for self-adjoint operators; 9. Essentially self-adjoint operators; 10. Discrete spectrum, essential spectrum; 11. The max-min principle; 12. An application to fluid mechanics; 13. Pseudospectra; 14. Applications for 1D-models; 15. Applications in kinetic theory; 16. Problems; References; Index.

Bernard Helffer is a Professor in the Department of Mathematics at Universite Paris-Sud. He has published more than 200 papers in mathematics and mathematical physics and authored five books. In 2011 he was awarded the Prix de l'Etat by the French Academy of Sciences.