Ordinary Differential Operators (Mathematical Surveys and Monographs, Band 245) - Hardcover

Wang, Aiping; Zettl, Anton

Hardcover

ISBN 10: 1470453665 ISBN 13: 9781470453664

Verlag: American Mathematical Society, 2020

Inhaltsangabe

In 1910 Herman Weyl published one of the most widely quoted papers of the 20th century in Analysis, which initiated the study of singular Sturm-Liouville problems. The work on the foundations of Quantum Mechanics in the 1920s and 1930s, including the proof of the spectral theorem for unbounded self-adjoint operators in Hilbert space by von Neumann and Stone, provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic developed in several directions and many results and applications have been obtained.

In this monograph the authors summarize some of these directions discussing self-adjoint, symmetric, and dissipative operators in Hilbert and Symplectic Geometry spaces. Part I of the book covers the theory of differential and quasi-differential expressions and equations, existence and uniqueness of solutions, continuous and differentiable dependence on initial data, adjoint expressions, the Lagrange Identity, minimal and maximal operators, etc. In Part II characterizations of the symmetric, self-adjoint, and dissipative boundary conditions are established. In particular, the authors prove the long standing Deficiency Index Conjecture. In Part III the symmetric and self-adjoint characterizations are extended to two-interval problems. These problems have solutions which have jump discontinuities in the interior of the underlying interval. These jumps may be infinite at singular interior points. Part IV is devoted to the construction of the regular Green's function. The construction presented differs from the usual one as found, for example, in the classical book by Coddington and Levinson.

Über diesen Titel

Über die Autorin bzw. den Autor

Aiping Wang, North China Electric Power University, Beijing, China.

Anton Zettl, Northern Illinois University, DeKalb, IL.

Details zur Ausgabe

• Verlag: American Mathematical Society
• Erscheinungsdatum: 2020
• Sprache: Englisch
• ISBN 10: 1470453665
• ISBN 13: 9781470453664
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 250
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: preigu; mail@preigu.de; ; Lengericher Landstr. 19; Osnabrück; 49078; Deutschland