Quantization, PDEs, and Geometry - The Interplay of Analysis and Mathematical Physics

This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.

Sommario

Introduction.- Todor Gramchev: Gelfand-Shilov Spaces: Structural Properties and Applications to Pseudodifferential Operators in R^n.- Miroslav Englis: An Excursion into Berezin-Toeplitz Quantization and Related Topics.- Andrew Comech: Global Attraction to Solitary Waves.- Irina Markina: Geodesics in Geometry with Constraints and Applications.

Riassunto

This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.

Dettagli sul prodotto

• Con la collaborazione di: Dorothea Bahns (Editore), Wolfra Bauer (Editore), Wolfram Bauer (Editore), Ingo Witt (Editore)
• Editore: Springer, Berlin
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 01.01.2018
• EAN: 9783319793962
• ISBN: 978-3-31-979396-2
• Pagine: 314
• Dimensioni: 153 mm x 234 mm x 18 mm
• Peso: 498 g
• Illustrazioni: VIII, 314 p. 16 illus., 5 illus. in color.
• Serie: Operator Theory: Advances and Applications; Advances in Partial Differential Equations; Operator Theory: Advances and Applications; Advances in Partial Differential Equations
• Categorie: Scienze naturali, medicina, informatica, tecnica > Matematica > Analisi; C, Mathematische Physik, Mathematische Analysis, allgemein, Mathematics and Statistics, Differential Geometry, Mathematical physics, Numerical analysis, Manifolds (Mathematics), Partial Differential Equations, Differential equations, Global analysis (Mathematics), Global Analysis and Analysis on Manifolds, Differential & Riemannian geometry, Calculus and mathematical analysis