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

Buch 2 von 23: Birkhäuser Advanced Texts Basler Lehrbücher

Krantz, Steven G.; Parks, Harold R.

 
9780817640972: The Geometry of Domains in Space (Birkhäuser Advanced Texts Basler Lehrbücher)
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.

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Über die Autorin bzw. den Autor

Steven G. Krantz is one of Springer's and Birkhäuser's most prolific and popular authors in the field of functional analysis, geometric analysis, and partial differential equations. Krantz is the series editor of Birkhäuser's ' Cornerstones' graduate text series and the founder and editor-in-chief of "The Journal of Geometric Analysis", considered a society journal previously published by the AMS and often acts as an advisor to several senior editors at Springer/ Birkhäuser . He is also editor-in-chief of the "Journal of Mathematical Analysis and Applications". Professor Krantz is currently the editor-in-chief of the AMS Notices and also edits for "The American Mathematical Monthly", "Complex Analysis and Elliptical Equations", and "The Bulletin of the American Mathematical Monthly". Krantz is also known for his wide breadth of expertise in several areas of mathematics such as harmonica analysis, differential geometry, and Lie groups, to name a few. Notable awards include Chauvenet Prize (1992), Beckenbach Book Award (1994), Kemper Prize (1994), Outstanding Academic Book Award (1998), Washington University Faculty Mentor Award (2007).

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Verlag
Birkhäuser
Erscheinungsdatum
1999
Sprache
Englisch
ISBN 10 
0817640975
ISBN 13 
9780817640972
Einband
Gebundene Ausgabe
Anzahl der Seiten
319
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