Fourier Mukai And Nahm Transforms In Geometry And Mathematical Physics

Author : CLAUDIO BARTOCCI
Publisher : Springer Science & Business Media
ISBN 13 : 0817646639
Total Pages : 435 pages
Book Rating : 4.39/5 ( download)

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Download or read book Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics written by CLAUDIO BARTOCCI and published by Springer Science & Business Media. This book was released on 2009-06-12 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry, category theory, gauge theory, and string theory has been closely related to generalizations of integral transforms of a more geometric character. "Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics" examines the algebro-geometric approach (Fourier–Mukai functors) as well as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organized into a monograph. Key features: Basic constructions and definitions are presented in preliminary background chapters - Presentation explores applications and suggests several open questions - Extensive bibliography and index. This self-contained monograph provides an introduction to current research in geometry and mathematical physics and is intended for graduate students and researchers just entering this field.

Author : Daniel Huybrechts
Publisher : Oxford University Press
ISBN 13 : 0199296863
Total Pages : 316 pages
Book Rating : 4.66/5 ( download)

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Download or read book Fourier-Mukai Transforms in Algebraic Geometry written by Daniel Huybrechts and published by Oxford University Press. This book was released on 2006-04-20 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is based on a course given at the Institut de Mathematiques de Jussieu, on the derived category of coherent sheaves on a smooth projective variety. It is aimed at students with a basic knowledge of algebraic geometry and contains full proofs and exercises that aid the reader.

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.27/5 ( download)

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Download or read book Nahm and Fourier--Mukai Transforms in Geometry and Mathematical Physics written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Daniel Huybrechts
Publisher :
ISBN 13 :
Total Pages : 307 pages
Book Rating : 4.13/5 ( download)

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Download or read book Fourier-Mukai Transforms in Algebraic Geometry written by Daniel Huybrechts and published by . This book was released on 2006 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : John Francis James
Publisher : Cambridge University Press
ISBN 13 : 9780521004282
Total Pages : 156 pages
Book Rating : 4.84/5 ( download)

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Download or read book A Student's Guide to Fourier Transforms written by John Francis James and published by Cambridge University Press. This book was released on 2002-09-19 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science.

Author : Alexander Koldobsky
Publisher : American Mathematical Soc.
ISBN 13 : 0821837877
Total Pages : 178 pages
Book Rating : 4.70/5 ( download)

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Download or read book Fourier Analysis in Convex Geometry written by Alexander Koldobsky and published by American Mathematical Soc.. This book was released on 2005 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to express certain geometric properties of bodies in terms of Fourier analysis and to use harmonic analysis methods to solve geometric problems. One of the results discussed in the book is Ball's theorem, establishing the exact upper bound for the $(n-1)$-dimensional volume of hyperplane sections of the $n$-dimensional unit cube (it is $\sqrt{2}$ for each $n\geq 2$). Another is the Busemann-Petty problem: if $K$ and $L$ are two convex origin-symmetric $n$-dimensional bodies and the $(n-1)$-dimensional volume of each central hyperplane section of $K$ is less than the $(n-1)$-dimensional volume of the corresponding section of $L$, is it true that the $n$-dimensional volume of $K$ is less than the volume of $L$? (The answer is positive for $n\le 4$ and negative for $n>4$.) The book is suitable for all mathematicians interested in geometry, harmonic and functional analysis, and probability. Prerequisites for reading this book include basic real, complex, and functional analysis.

Author : Valery Serov
Publisher : Springer
ISBN 13 : 3319652621
Total Pages : 534 pages
Book Rating : 4.27/5 ( download)

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Download or read book Fourier Series, Fourier Transform and Their Applications to Mathematical Physics written by Valery Serov and published by Springer. This book was released on 2017-11-26 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences. Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing. The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations. The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory of partial differential equations. Complete with nearly 250 exercises throughout, this text is intended for graduate level students and researchers in the mathematical sciences and engineering.

Author : Jorge L. Delyra
Publisher : Mathematical Methods for Physi
ISBN 13 : 9781796836295
Total Pages : 348 pages
Book Rating : 4.9X/5 ( download)

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Download or read book Fourier Transforms: Mathematical Methods for Physics and Engineering - written by Jorge L. Delyra and published by Mathematical Methods for Physi. This book was released on 2019-02-15 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a longstanding conflict between extension and depth in the teaching of mathematics to physics students. This text intends to present an approach that tries to track what could be called the ``middle way'' in this conflict. It is the result of several years of experience of the author teaching the mathematical physics courses at the Physics Institute of the University of São Paulo. The text is organized in the form of relatively short chapters, each appropriate for exposition in one lecture. Each chapter includes a list of proposed problems, which have varied levels of difficulty, including practice problems, problems that complete and extend the material presented in the text, and some longer and more difficult problems, which are presented as challenges to the students. There are complete solutions available, detailed and commented, to all the problems proposed, which are presented in separate volumes. This volume is dedicated to Fourier transforms. This term is used here in a wider sense, including finite Fourier transforms, defined on a finite and discrete lattice, Fourier series, defined on a finite domain within the continuum, and the usual Fourier transforms, defined on the infinite continuum. This constitutes an elementary introduction to what is called, in its more abstract form, harmonic analysis. By means of the device of starting from the finite and discrete version of the formalism, which is done in the spirit of the definition of the Riemann integral, we are able to present in a clear way the basic structure of this whole formalism, while avoiding any need to face on this first moment the difficult convergence questions that arise when one takes the continuum limit. Once in the continuum, the convergence issues are addressed and put in proper perspective through the use of a low-pass filter, which is defined and developed in a fairly precise way. In the last two chapters the whole structure of the Fourier theory of real functions is derived ``ab initio'' once again, this time directly in the continuum, starting from the theory of analytic functions. There we present something that works like a universal summation rule, which applies to all Fourier series, and which allows us to recover any integrable real function from the set of its Fourier coefficients, even when the Fourier series itself diverges.

Author : Fritz Oberhettinger
Publisher : Springer Science & Business Media
ISBN 13 : 3642743498
Total Pages : 261 pages
Book Rating : 4.98/5 ( download)

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Download or read book Tables of Fourier Transforms and Fourier Transforms of Distributions written by Fritz Oberhettinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of integrals of the sine-, cosine- and exponential Fourier transforms of functions f(x). It is the second, considerably enlarged version of the author's previous publication "Tabellen zur Fourier Transformation" (Springer-Verlag 1957). In addition to numerous new results in Parts I-III, a new Part IV has been introduced dealing with problems in mathematical statistics. The aim of the book is to serve as a reference work for all those whose main interest is in the application of Fourier transform methods. These methods have found a wide variety of applications in the natural and technical sciences.

Author : Michael Reed
Publisher : Elsevier
ISBN 13 : 9780125850025
Total Pages : 388 pages
Book Rating : 4.26/5 ( download)

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Download or read book II: Fourier Analysis, Self-Adjointness written by Michael Reed and published by Elsevier. This book was released on 1975 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Band 2.