Expansions in Eigenfunctions of Selfadjoint Operators
Author: I͡Uriĭ Makarovich Berezanskiĭ
Publisher: American Mathematical Soc.
Published: 1968
Total Pages: 824
ISBN-13: 9780821886496
DOWNLOAD EBOOKRead and Download eBook Full
Author: I͡Uriĭ Makarovich Berezanskiĭ
Publisher: American Mathematical Soc.
Published: 1968
Total Pages: 824
ISBN-13: 9780821886496
DOWNLOAD EBOOKAuthor: I_Uri_ Makarovich Berezanski_
Publisher: American Mathematical Soc.
Published: 1986-12-31
Total Pages: 404
ISBN-13: 9780821898130
DOWNLOAD EBOOKQuestions in the spectral theory of selfadjoint and normal operators acting in spaces of functions of infinitely many variables are studied in this book, and, in particular, the theory of expansions in generalized eigenfunctions of such operators. Both individual operators and arbitrary commuting families of them are considered. A theory of generalized functions of infinitely many variables is constructed. The circle of questions presented has evolved in recent years, especially in connection with problems in quantum field theory. This book will be useful to mathematicians and physicists interested in the indicated questions, as well as to graduate students and students in advanced university courses.
Author:
Publisher:
Published: 1968
Total Pages: 0
ISBN-13: 9781470444358
DOWNLOAD EBOOKAuthor: RAINER DICK
Publisher: Springer
Published: 2016-07-01
Total Pages: 694
ISBN-13: 3319256750
DOWNLOAD EBOOKIn this updated and expanded second edition of a well-received and invaluable textbook, Prof. Dick emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. Advanced Quantum Mechanics, Materials and Photons can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. This second edition includes an additional 62 new problems as well as expanded sections on relativistic quantum fields and applications of quantum electrodynamics. Other special features include an introduction to Lagrangian field theory and an integrated discussion of transition amplitudes with discrete or continuous initial or final states. Once students have acquired an understanding of basic quantum mechanics and classical field theory, canonical field quantization is easy. Furthermore, the integrated discussion of transition amplitudes naturally leads to the notions of transition probabilities, decay rates, absorption cross sections and scattering cross sections, which are important for all experimental techniques that use photon probes.
Author: R. Mennicken
Publisher: Gulf Professional Publishing
Published: 2003-06-26
Total Pages: 536
ISBN-13: 9780444514479
DOWNLOAD EBOOKThe 'North-Holland Mathematics Studies' series comprises a set of cutting-edge monographs and studies. This volume explores non-self-adjoint boundary eigenvalue problems for first order systems of ordinary differential equations and n-th order scalar differential equations.
Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
Published: 2013-12-01
Total Pages: 555
ISBN-13: 9400959915
DOWNLOAD EBOOKThis ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Author: M. Hazewinkel
Publisher: Springer
Published: 2013-12-01
Total Pages: 932
ISBN-13: 1489937919
DOWNLOAD EBOOKAuthor: F.V. Atkinson
Publisher: CRC Press
Published: 2010-12-07
Total Pages: 297
ISBN-13: 1439816239
DOWNLOAD EBOOKOne of the masters in the differential equations community, the late F.V. Atkinson contributed seminal research to multiparameter spectral theory and Sturm-Liouville theory. His ideas and techniques have long inspired researchers and continue to stimulate discussion. With the help of co-author Angelo B. Mingarelli, Multiparameter Eigenvalue Problem
Author: Joseph A. Ball
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 604
ISBN-13: 3034878818
DOWNLOAD EBOOKMany developments on the cutting edge of research in operator theory and its applications are reflected in this collection of original and review articles. Particular emphasis lies on highlighting the interplay between operator theory and applications from other areas, such as multi-dimensional systems and function theory of several complex variables, distributed parameter systems and control theory, mathematical physics, wavelets, and numerical analysis.
Author: Oktay Veliev
Publisher: Springer Nature
Published: 2021-06-19
Total Pages: 301
ISBN-13: 3030726835
DOWNLOAD EBOOKThis book gives a complete spectral analysis of the non-self-adjoint Schrödinger operator with a periodic complex-valued potential. Building from the investigation of the spectrum and spectral singularities and construction of the spectral expansion for the non-self-adjoint Schrödinger operator, the book features a complete spectral analysis of the Mathieu-Schrödinger operator and the Schrödinger operator with a parity-time (PT)-symmetric periodic optical potential. There currently exists no general spectral theorem for non-self-adjoint operators; the approaches in this book thus open up new possibilities for spectral analysis of some of the most important operators used in non-Hermitian quantum mechanics and optics. Featuring detailed proofs and a comprehensive treatment of the subject matter, the book is ideally suited for graduate students at the intersection of physics and mathematics.