Unbounded Self-adjoint Operators on Hilbert Space (Graduate Texts in Mathematics, #265)
by Konrad Schmuedgen
The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises. The main themes of the book are the following:...
The Schrödinger Equation (Mathematics and its Applications, #66)
by F. A. Berezin and M A Shubin
4Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non* The series is divergent; therefore we may be sense'. able to do something withit. Eric T. Bell O. Heaviside Mathematicsis a tool for thought. A highly necessary tool in a world whereboth feedback and non- linearities abound. Similarly, all...
Analysis 1 (Springer-Lehrbuch) (Grundwissen Mathematik, #3)
by Wolfgang Walter
Aus den Besprechungen: "Wodurch unterscheidet sich das hiermit begonnene Lehrwerk der Analysis von zahlreichen anderen ... exzellenten Werken dieser Art? ... (1) die ausfuhrliche Berucksichtigung des Warum und Woher, der historischen Gesichtspunkte ...; (2) die Anerkennung der Existenz des Computers. Der Autor verschliesst sich nicht vor der Tatsache, dass die Computermathematik (hier vor allem verstanden als numerische Mathematik) oft interessante Anwendungen der klassischen Analysis bietet. ....
Modern Sampling Theory (Applied and Numerical Harmonic Analysis)
A state-of-the-art edited survey covering all aspects of sampling theory. Theory, methods and applications are discussed in authoritative expositions ranging from multi-dimensional signal analysis to wavelet transforms. The book is an essential up-to-date resource.
Overview Historically, the concept of "ondelettes" or "wavelets" originated from the study of time-frequency signal analysis, wave propagation, and sampling theory. One of the main reasons for the discovery of wavelets and wavelet transforms is that the Fourier transform analysis does not contain the local information of signals. So the Fourier transform cannot be used for analyzing signals in a joint time and frequency domain. In 1982, Jean MorIet, in collaboration with a group of French engine...
Conformable Dynamic Equations on Time Scales
by Douglas R. Anderson and Svetlin G. Georgiev
The concept of derivatives of non-integer order, known as fractional derivatives, first appeared in the letter between L’Hopital and Leibniz in which the question of a half-order derivative was posed. Since then, many formulations of fractional derivatives have appeared. Recently, a new definition of fractional derivative, called the "fractional conformable derivative," has been introduced. This new fractional derivative is compatible with the classical derivative and it has attracted attention...
A Modern Approach to Functional Integration (Applied and Numerical Harmonic Analysis)
by John R Klauder
This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a...
Measure Theory and Integration, Second Edition (Chapman & Hall/CRC Pure and Applied Mathematics)
by M M Rao
Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types-providing a complete and detailed review of every aspect of measure and integration theory using valuable examples, exercises, and applications. With more than 170 references for further investigation of the subject, this Second Edition provides more than 60 pages of new information...
This book is based on an International Conference on Trends in Theory and Practice of Nonlinear Differential Equations held at The University of Texas at Arlington. It aims to feature recent trends in theory and practice of nonlinear differential equations.
Potential Theory on Sierpiński Carpets (Lecture Notes in Mathematics, #2268)
by Dimitrios Ntalampekos
This self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpiński carpets, and proposes a theory based on the latest developments in the field of analysis on metric spaces. The first part focuses on the development of an innovative theory of harmonic functions that is suitable for Sierpiński carpets but differs from the classical approach of potential theory in metric spaces. The second part describes how this th...
Harmonic Analysis of Operators on Hilbert Space (Universitext)
by B La Sz -Nagy, Ciprian Foias, and Hari Bercovici
The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, includi...
Neutrices and External Numbers (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by Bruno Dinis and Imme van den Berg
Neutrices and External Numbers: A Flexible Number System introduces a new model of orders of magnitude and of error analysis, with particular emphasis on behaviour under algebraic operations. The model is formulated in terms of scalar neutrices and external numbers, in the form of an extension of the nonstandard set of real numbers. Many illustrative examples are given. The book starts with detailed presentation of the algebraic structure of external numbers, then deals with the generalized Dede...
Some Sequence Spaces and Their Geometric Properties
by Vakeel A. Khan
The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schroedinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will b...
Noncompact Semisimple Lie Algebras and Groups (De Gruyter Studies in Mathematical Physics)
by Vladimir K. Dobrev
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schroedinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory supplemented by many concrete examples for a great variety of noncompact semisimple Lie algebras and groups. Contents:...
Approximation of Additive Convolution-Like Operators (Frontiers in Mathematics)
by Victor D Didenko and Bernd Silbermann
This book deals with numerical analysis for certain classes of additive operators and related equations, including singular integral operators with conjugation, the Riemann-Hilbert problem, Mellin operators with conjugation, double layer potential equation, and the Muskhelishvili equation. The authors propose a unified approach to the analysis of the approximation methods under consideration based on special real extensions of complex C*-algebras. The list of the methods considered includes spli...
Harmonic Analysis of Schroedinger Operators (Advances in Analysis and Geometry)
by Shijun Zheng and Jiqiang Zheng
Focusing on harmonic analysis problems related to Schroedinger operators, this book presents state-of-the-art methods and techniques in harmonic analysis along with functional and nonlinear analysis in phase space. Moreover, applications in linear and nonlinear partial differential equations are discussed in detail. With extensive examples, this book is an essential reference to researchers and graduate students working in the field.
Functional Analysis for Probability and Stochastic Processes: An Introduction
by Adam Bobrowski
In recent years, the fixed point theory of Lipschitzian-type mappings has rapidly grown into an important field of study in both pure and applied mathematics. It has become one of the most essential tools in nonlinear functional analysis. This self-contained book provides the first systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. The first chapter covers some basic properties of metric and Banach spaces. Geometric considerations of underlying spaces play a prom...