The Geometry of Domains in Space (Birkhäuser Advanced Texts Basler Lehrbücher) - Hardcover

Krantz, Steven G.; Parks, Harold R.

Hardcover

ISBN 10: 0817640975 ISBN 13: 9780817640972

Verlag: Birkhäuser, 1999

Inhaltsangabe

The analysis of Euclidean space is well-developed. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans­ lations-have both shaped and guided this development. In particular, the Fourier transform and the theory of translation invariant operators (convolution transforms) have played a central role in this analysis. Much modern work in analysis takes place on a domain in space. In this context the tools, perforce, must be different. No longer can we expect there to be symmetries. Correspondingly, there is no longer any natural way to apply the Fourier transform. Pseudodifferential operators and Fourier integral operators can playa role in solving some of the problems, but other problems require new, more geometric, ideas. At a more basic level, the analysis of a smoothly bounded domain in space requires a great deal of preliminary spadework. Tubular neighbor­ hoods, the second fundamental form, the notion of "positive reach", and the implicit function theorem are just some of the tools that need to be invoked regularly to set up this analysis. The normal and tangent bundles become part of the language of classical analysis when that analysis is done on a domain. Many of the ideas in partial differential equations-such as Egorov's canonical transformation theorem-become rather natural when viewed in geometric language. Many of the questions that are natural to an analyst-such as extension theorems for various classes of functions-are most naturally formulated using ideas from geometry.

Über diesen Titel

Über die Autorin bzw. den Autor

Peter V. Dovbush is an Associate Professor and Leading Researcher at the Institute of Mathematics and Computer Science of Moldova State University, Moldova. His research interests lie on the geometric theory of functions of several complex variables. Steven G. Krantz earned his B.A. from the University of California at Santa Cruz (1971) and his PhD from Princeton University, USA (1974). With teaching periods at UCLA, Princeton, Penn State, and Washington University in St. Louis, he chaired the latter's mathematics department for five years. Dr. Krantz has authored or co-authored over 160 books and 350 scholarly papers, and he has edited numerous journals. His contributions to mathematics have earned him awards such as the Chauvenet Prize, the Beckenbach Book Award, and the Kemper Prize.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 1999
• Sprache: Englisch
• ISBN 10: 0817640975
• ISBN 13: 9780817640972
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 319
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland