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Mathematics Past And Present Fourier Integral Operators


Mathematics Past And Present Fourier Integral Operators
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Mathematics Past And Present Fourier Integral Operators


Mathematics Past And Present Fourier Integral Operators
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Author : Jochen Brüning
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Mathematics Past And Present Fourier Integral Operators written by Jochen Brüning and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.


What is the true mark of inspiration? Ideally it may mean the originality, freshness and enthusiasm of a new breakthrough in mathematical thought. The reader will feel this inspiration in all four seminal papers by Duistermaat, Guillemin and Hörmander presented here for the first time ever in one volume. However, as time goes by, the price researchers have to pay is to sacrifice simplicity for the sake of a higher degree of abstraction. Thus the original idea will only be a foundation on which more and more abstract theories are being built. It is the unique feature of this book to combine the basic motivations and ideas of the early sources with knowledgeable and lucid expositions on the present state of Fourier Integral Operators, thus bridging the gap between the past and present. A handy and useful introduction that will serve novices in this field and working mathematicians equally well.



Mathematics Past And Present Fourier Integral Operators


Mathematics Past And Present Fourier Integral Operators
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Author : Jochen Brüning
language : en
Publisher: Springer
Release Date : 2010-12-01

Mathematics Past And Present Fourier Integral Operators written by Jochen Brüning and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-01 with Mathematics categories.


What is the true mark of inspiration? Ideally it may mean the originality, freshness and enthusiasm of a new breakthrough in mathematical thought. The reader will feel this inspiration in all four seminal papers by Duistermaat, Guillemin and Hörmander presented here for the first time ever in one volume. However, as time goes by, the price researchers have to pay is to sacrifice simplicity for the sake of a higher degree of abstraction. Thus the original idea will only be a foundation on which more and more abstract theories are being built. It is the unique feature of this book to combine the basic motivations and ideas of the early sources with knowledgeable and lucid expositions on the present state of Fourier Integral Operators, thus bridging the gap between the past and present. A handy and useful introduction that will serve novices in this field and working mathematicians equally well.



Mathematics Past And Present Fourier Integral Operators


Mathematics Past And Present Fourier Integral Operators
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Author : Jochen Brüning
language : en
Publisher: Springer
Release Date : 2012-12-22

Mathematics Past And Present Fourier Integral Operators written by Jochen Brüning and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-22 with Mathematics categories.


What is the true mark of inspiration? Ideally it may mean the originality, freshness and enthusiasm of a new breakthrough in mathematical thought. The reader will feel this inspiration in all four seminal papers by Duistermaat, Guillemin and Hörmander presented here for the first time ever in one volume. However, as time goes by, the price researchers have to pay is to sacrifice simplicity for the sake of a higher degree of abstraction. Thus the original idea will only be a foundation on which more and more abstract theories are being built. It is the unique feature of this book to combine the basic motivations and ideas of the early sources with knowledgeable and lucid expositions on the present state of Fourier Integral Operators, thus bridging the gap between the past and present. A handy and useful introduction that will serve novices in this field and working mathematicians equally well.



Mathematics Past And Present


Mathematics Past And Present
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Author : Johannes Jisse Duistermaat
language : en
Publisher:
Release Date : 1994

Mathematics Past And Present written by Johannes Jisse Duistermaat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Fourier integral operators categories.




Fourier Integral Operators


Fourier Integral Operators
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Author : J.J. Duistermaat
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-11-29

Fourier Integral Operators written by J.J. Duistermaat and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-29 with Mathematics categories.


This volume is a useful introduction to the subject of Fourier Integral Operators and is based on the author’s classic set of notes. Covering a range of topics from Hörmander’s exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes application to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially in wave propagation, rep. WKB-methods.



The Analysis Of Linear Partial Differential Operators Iv


The Analysis Of Linear Partial Differential Operators Iv
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Author : Lars Hörmander
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-28

The Analysis Of Linear Partial Differential Operators Iv written by Lars Hörmander and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-28 with Mathematics categories.


From the reviews: "Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators." L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987 "This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation." J. Brüning in Zentralblatt MATH, 1987 Honours awarded to Lars Hörmander: Fields Medal 1962, Speaker at International Congress 1970, Wolf Prize 1988, AMS Steele Prize 2006



Lectures On The Geometry Of Quantization


Lectures On The Geometry Of Quantization
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Author : Sean Bates
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Lectures On The Geometry Of Quantization written by Sean Bates and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.


These notes are based on a course entitled ``Symplectic Geometry and Geometric Quantization'' taught by Alan Weinstein at the University of California, Berkeley (fall 1992) and at the Centre Emile Borel (spring 1994). The only prerequisite for the course needed is a knowledge of the basic notions from the theory of differentiable manifolds (differential forms, vector fields, transversality, etc.). The aim is to give students an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and quantum mechanics (unitary flows on Hilbert spaces). These notes are meant to function as a guide to the literature. The authors refer to other sources for many details that are omitted and can be bypassed on a first reading.



Theory And Applications Of Models Of Computation


Theory And Applications Of Models Of Computation
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Author : Manindra Agrawal
language : en
Publisher: Springer
Release Date : 2012-05-04

Theory And Applications Of Models Of Computation written by Manindra Agrawal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-04 with Computers categories.


This book constitutes the refereed proceedings of the 9th International Conference on Theory and Applications of Models of Computation, TAMC 2012, held in Beijing, China, in May 2012. The conference was combined with the Turing Lectures 2012, dedicated to celebrating Alan Turing’s unique impact on mathematics, computing, computer science, informatics, morphogenesis, philosophy, and the wider scientific world. Eight Turing Lectures were given at the TAMC 2012. The 40 revised full papers presented together with invited talks were carefully reviewed and selected from 86 submissions. The papers address 4 special sessions at TAMC 2012 which were algorithms and information in networks, complexity and cryptography, models of computing and networking, programming and verification.



Pseudodifferential Operators And Spectral Theory


Pseudodifferential Operators And Spectral Theory
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Author : M.A. Shubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28

Pseudodifferential Operators And Spectral Theory written by M.A. Shubin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Mathematics categories.


I had mixed feelings when I thought how I should prepare the book for the second edition. It was clear to me that I had to correct all mistakes and misprints that were found in the book during the life of the first edition. This was easy to do because the mistakes were mostly minor and easy to correct, and the misprints were not many. It was more difficult to decide whether I should update the book (or at least its bibliography) somehow. I decided that it did not need much of an updating. The main value of any good mathematical book is that it teaches its reader some language and some skills. It can not exhaust any substantial topic no matter how hard the author tried. Pseudodifferential operators became a language and a tool of analysis of partial differential equations long ago. Therefore it is meaningless to try to exhaust this topic. Here is an easy proof. As of July 3, 2000, MathSciNet (the database of the American Mathematical Society) in a few seconds found 3695 sources, among them 363 books, during its search for "pseudodifferential operator". (The search also led to finding 963 sources for "pseudo-differential operator" but I was unable to check how much the results ofthese two searches intersected). This means that the corresponding words appear either in the title or in the review published in Mathematical Reviews.



Fourier Integrals In Classical Analysis


Fourier Integrals In Classical Analysis
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Author : Christopher D. Sogge
language : en
Publisher: Cambridge University Press
Release Date : 2008-04-24

Fourier Integrals In Classical Analysis written by Christopher D. Sogge and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-24 with Mathematics categories.


Fourier Integrals in Classical Analysis is an advanced treatment of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. Using microlocal analysis, the author in particular studies problems involving maximal functions and Riesz means using the so-called half-wave operator. This self-contained book starts with a rapid review of important topics in Fourier analysis. The author then presents the necessary tools from microlocal analysis, and goes on to give a proof of the sharp Weyl formula which he then modifies to give sharp estimates for the size of eigenfunctions on compact manifolds. Finally, the tools that have been developed are used to study the regularity properties of Fourier integral operators, culminating in the proof of local smoothing estimates and their applications to singular maximal theorems in two and more dimensions.