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Spectral Theory and Differential Operators

2018 Mathematics
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Release : 2018
Genre : Mathematics
Kind : eBook
Book Rating : 051/5 ( reviews)

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Book Synopsis Spectral Theory and Differential Operators by : David Eric Edmunds

Download or read book Spectral Theory and Differential Operators written by David Eric Edmunds. This book was released on 2018. Available in PDF, EPUB and Kindle. Book excerpt: This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.

Partial Differential Equations VII

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 196/5 ( reviews)

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Book Synopsis Partial Differential Equations VII by : M.A. Shubin

Download or read book Partial Differential Equations VII written by M.A. Shubin. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. Also including a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum".

Spectral Theory of Ordinary Differential Operators

2006-11-15 Mathematics
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Release : 2006-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 120/5 ( reviews)

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Book Synopsis Spectral Theory of Ordinary Differential Operators by : Joachim Weidmann

Download or read book Spectral Theory of Ordinary Differential Operators written by Joachim Weidmann. This book was released on 2006-11-15. Available in PDF, EPUB and Kindle. Book excerpt: These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions existence and construction of self-adjoint realizations via boundary conditions, determination and study of general properties of the resolvent, spectral representation and spectral resolution. Special attention is paid to the question of separated boundary conditions, spectral multiplicity and absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville operators and Dirac systems) the classical theory of Weyl-Titchmarch is included. Oscillation theory for Sturm-Liouville operators and Dirac systems is developed and applied to the study of the essential and absolutely continuous spectrum. The results are illustrated by the explicit solution of a number of particular problems including the spectral theory one partical Schrödinger and Dirac operators with spherically symmetric potentials. The methods of proof are functionally analytic wherever possible.

Pseudodifferential Operators and Spectral Theory

2011-06-28 Mathematics
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Release : 2011-06-28
Genre : Mathematics
Kind : eBook
Book Rating : 794/5 ( reviews)

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Book Synopsis Pseudodifferential Operators and Spectral Theory by : M.A. Shubin

Download or read book Pseudodifferential Operators and Spectral Theory written by M.A. Shubin. This book was released on 2011-06-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral Theory and Differential Operators

1995 Mathematics
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Release : 1995
Genre : Mathematics
Kind : eBook
Book Rating : 105/5 ( reviews)

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Book Synopsis Spectral Theory and Differential Operators by : E. Brian Davies

Download or read book Spectral Theory and Differential Operators written by E. Brian Davies. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on partial differential operators.

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