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The Convenient Setting of Global Analysis

1997 Mathematics
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Release : 1997
Genre : Mathematics
Kind : eBook
Book Rating : 803/5 ( reviews)

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Book Synopsis The Convenient Setting of Global Analysis by : Andreas Kriegl

Download or read book The Convenient Setting of Global Analysis written by Andreas Kriegl. This book was released on 1997. Available in PDF, EPUB and Kindle. Book excerpt: For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR

Handbook of Global Analysis

2011-08-11 Mathematics
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Release : 2011-08-11
Genre : Mathematics
Kind : eBook
Book Rating : 736/5 ( reviews)

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Book Synopsis Handbook of Global Analysis by : Demeter Krupka

Download or read book Handbook of Global Analysis written by Demeter Krupka. This book was released on 2011-08-11. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents

Geometric and Algebraic Topological Methods in Quantum Mechanics

2005 Science
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Release : 2005
Genre : Science
Kind : eBook
Book Rating : 293/5 ( reviews)

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Book Synopsis Geometric and Algebraic Topological Methods in Quantum Mechanics by : G. Giachetta

Download or read book Geometric and Algebraic Topological Methods in Quantum Mechanics written by G. Giachetta. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: - The book collects all the advanced methods of quantization in the last decade. - It presents in a compact way all the necessary up to date mathematical tools to be used in studying quantum problems.

Morita Equivalence and Continuous-Trace $C^*$-Algebras

1998 Mathematics
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Release : 1998
Genre : Mathematics
Kind : eBook
Book Rating : 605/5 ( reviews)

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Book Synopsis Morita Equivalence and Continuous-Trace $C^*$-Algebras by : Iain Raeburn

Download or read book Morita Equivalence and Continuous-Trace $C^*$-Algebras written by Iain Raeburn. This book was released on 1998. Available in PDF, EPUB and Kindle. Book excerpt: A modern treatment of this complex mathematical topic for students beginning research in operator algebras as well as mathematical physicists. Topics include the algebra of compact operators, sheaves, cohomology, the Brauer group and group actions, and the imprimivity theorem. The authors assume a knowledge of C*-algebras, the Gelfand-Naimark Theorem, continuous functional calculus, positivity, and the GNS- construction. Annotation copyrighted by Book News, Inc., Portland, OR

Number Theoretic Density and Logical Limit Laws

2001 Mathematics
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Release : 2001
Genre : Mathematics
Kind : eBook
Book Rating : 662/5 ( reviews)

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Book Synopsis Number Theoretic Density and Logical Limit Laws by : Stanley Burris

Download or read book Number Theoretic Density and Logical Limit Laws written by Stanley Burris. This book was released on 2001. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how a study of generating series (power series in the additive case and Dirichlet series in the multiplicative case), combined with structure theorems for the finite models of a sentence, lead to general and powerful results on limit laws, including 0 - 1 laws. The book is unique in its approach to giving a combined treatment of topics from additive as well as from multiplicative number theory, in the setting of abstract number systems, emphasizing the remarkable parallels in the two subjects. Much evidence is collected to support the thesis that local results in additive systems lift to global results in multiplicative systems. All necessary material is given to understand thoroughly the method of Compton for proving logical limit laws, including a full treatment of Ehrenfeucht-Fraissé games, the Feferman-Vaught Theorem, and Skolem's quantifier elimination for finite Boolean algebras. An intriguing aspect of the book is to see so many interesting tools from elementary mathematics pull together to answer the question: What is the probability that a randomly chosen structure has a given property? Prerequisites are undergraduate analysis and some exposure to abstract systems.

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