Studies in Advanced Mathematics
Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem
1st Edition
By Peter B. Gilkey
December 22, 1994
This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the ...
Wavelets: Mathematics and Applications
1st Edition
Edited
By John J. Benedetto
September 27, 1993
Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast ...
An Introduction to Operator Algebras
1st Edition
By Kehe Zhu
May 27, 1993
An Introduction to Operator Algebras is a concise text/reference that focuses on the fundamental results in operator algebras. Results discussed include Gelfand's representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann's double ...
Elementary Introduction to the Theory of Pseudodifferential Operators
1st Edition
By Xavier Saint Raymond
September 17, 1991
In the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This ...