A Guide To Spectral Theory PDF Download
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Author | : Christophe Cheverry |
Publisher | : Springer Nature |
Total Pages | : 258 |
Release | : 2021-05-06 |
Genre | : Mathematics |
ISBN | : 3030674622 |
Download A Guide to Spectral Theory Book in PDF, ePub and Kindle
This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.
Author | : Robin Harte |
Publisher | : Springer |
Total Pages | : 132 |
Release | : 2014-04-29 |
Genre | : Mathematics |
ISBN | : 3319056484 |
Download Spectral Mapping Theorems Book in PDF, ePub and Kindle
Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several and many variables. The basic algebraic systems – semigroups, rings and linear algebras – are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Spectral Mapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory.
Author | : John McCleary |
Publisher | : Cambridge University Press |
Total Pages | : 579 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0521567599 |
Download A User's Guide to Spectral Sequences Book in PDF, ePub and Kindle
Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.
Author | : David Eric Edmunds |
Publisher | : Oxford University Press |
Total Pages | : 610 |
Release | : 2018 |
Genre | : Mathematics |
ISBN | : 0198812051 |
Download Spectral Theory and Differential Operators Book in PDF, ePub and Kindle
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.--
Author | : R. Carmona |
Publisher | : Springer Science & Business Media |
Total Pages | : 611 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461244889 |
Download Spectral Theory of Random Schrödinger Operators Book in PDF, ePub and Kindle
Since the seminal work of P. Anderson in 1958, localization in disordered systems has been the object of intense investigations. Mathematically speaking, the phenomenon can be described as follows: the self-adjoint operators which are used as Hamiltonians for these systems have a ten dency to have pure point spectrum, especially in low dimension or for large disorder. A lot of effort has been devoted to the mathematical study of the random self-adjoint operators relevant to the theory of localization for disordered systems. It is fair to say that progress has been made and that the un derstanding of the phenomenon has improved. This does not mean that the subject is closed. Indeed, the number of important problems actually solved is not larger than the number of those remaining. Let us mention some of the latter: • A proof of localization at all energies is still missing for two dimen sional systems, though it should be within reachable range. In the case of the two dimensional lattice, this problem has been approached by the investigation of a finite discrete band, but the limiting pro cedure necessary to reach the full two-dimensional lattice has never been controlled. • The smoothness properties of the density of states seem to escape all attempts in dimension larger than one. This problem is particularly serious in the continuous case where one does not even know if it is continuous.
Author | : L. H. Koopmans |
Publisher | : Academic Press |
Total Pages | : 383 |
Release | : 2014-05-12 |
Genre | : Mathematics |
ISBN | : 1483218546 |
Download The Spectral Analysis of Time Series Book in PDF, ePub and Kindle
The Spectral Analysis of Time Series describes the techniques and theory of the frequency domain analysis of time series. The book discusses the physical processes and the basic features of models of time series. The central feature of all models is the existence of a spectrum by which the time series is decomposed into a linear combination of sines and cosines. The investigator can used Fourier decompositions or other kinds of spectrals in time series analysis. The text explains the Wiener theory of spectral analysis, the spectral representation for weakly stationary stochastic processes, and the real spectral representation. The book also discusses sampling, aliasing, discrete-time models, linear filters that have general properties with applications to continuous-time processes, and the applications of multivariate spectral models. The text describes finite parameter models, the distribution theory of spectral estimates with applications to statistical inference, as well as sampling properties of spectral estimates, experimental design, and spectral computations. The book is intended either as a textbook or for individual reading for one-semester or two-quarter course for students of time series analysis users. It is also suitable for mathematicians or professors of calculus, statistics, and advanced mathematics.
Author | : Harry Dym |
Publisher | : Courier Corporation |
Total Pages | : 354 |
Release | : 2008-01-01 |
Genre | : Mathematics |
ISBN | : 048646279X |
Download Gaussian Processes, Function Theory, and the Inverse Spectral Problem Book in PDF, ePub and Kindle
This text offers background in function theory, Hardy functions, and probability as preparation for surveys of Gaussian processes, strings and spectral functions, and strings and spaces of integral functions. It addresses the relationship between the past and the future of a real, one-dimensional, stationary Gaussian process. 1976 edition.
Author | : S. Lawrence Marple, Jr. |
Publisher | : Courier Dover Publications |
Total Pages | : 435 |
Release | : 2019-03-20 |
Genre | : Technology & Engineering |
ISBN | : 048678052X |
Download Digital Spectral Analysis Book in PDF, ePub and Kindle
Digital Spectral Analysis offers a broad perspective of spectral estimation techniques and their implementation. Coverage includes spectral estimation of discrete-time or discrete-space sequences derived by sampling continuous-time or continuous-space signals. The treatment emphasizes the behavior of each spectral estimator for short data records and provides over 40 techniques described and available as implemented MATLAB functions. In addition to summarizing classical spectral estimation, this text provides theoretical background and review material in linear systems, Fourier transforms, matrix algebra, random processes, and statistics. Topics include Prony's method, parametric methods, the minimum variance method, eigenanalysis-based estimators, multichannel methods, and two-dimensional methods. Suitable for advanced undergraduates and graduate students of electrical engineering — and for scientific use in the signal processing application community outside of universities — the treatment's prerequisites include some knowledge of discrete-time linear system and transform theory, introductory probability and statistics, and linear algebra. 1987 edition.
Author | : Steven G. Krantz |
Publisher | : MAA |
Total Pages | : 151 |
Release | : 2013-06-06 |
Genre | : Mathematics |
ISBN | : 0883853574 |
Download A Guide to Functional Analysis Book in PDF, ePub and Kindle
This book is a quick but precise and careful introduction to the subject of functional analysis. It covers the basic topics that can be found in a basic graduate analysis text. But it also covers more sophisticated topics such as spectral theory, convexity, and fixed-point theorems. A special feature of the book is that it contains a great many examples and even some applications. It concludes with a statement and proof of Lomonosov's dramatic result about invariant subspaces.
Author | : M. Sh. Birman |
Publisher | : Springer Science & Business Media |
Total Pages | : 96 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 1468475894 |
Download Spectral Theory Book in PDF, ePub and Kindle