Series: Operator Theory: Advances and Applications, Vol. 224
2012, 2012, Approx. 250 p.
Hardcover, ISBN 978-3-0348-0413-4
Due: May 31, 2012
This volume contains surveys as well as research articles broadly centered on spectral analysis. Topics range from spectral continuity for magnetic and pseudodifferential operators to localization in random media, from the stability of matter to properties of Aharonov-Bohm and Quantum Hall Hamiltonians, from waveguides and resonances to supersymmetric models and dissipative fermion systems. This is the first of a series of volumes reporting every two years on recent progress in spectral theory.
Preface.- Asch/Bourget/Cortes/: Resonant behaviors for some time dependent quantum systems: some remarks.- Belmonte/M?ntoiu: Continuity of Spectra in Rieffel’s Pseudodifferential Calculus.- Benguria: Stability of Matter.- Cornean/Purice: On the regularity of the Hausdorff distance between spectra of perturbed magnetic Hamiltonians.- De Nittis/Panati: The topological Bloch-Floquet transform and some applications.- Elgart/Kruger/Tautenhahn/Veselic: Discrete Schrodinger operators with random alloy-type potential.- Falomir/Pisani: Operator Domains and SUSY Breaking in a Model of SUSYQM with a Singular Potential.- Gorka/Prado/Reyes: Generalized euclidean bosonic string equations.- Klopp: Resonances for “Large” Ergodic Systems in One Dimension: a Review.- Klopp/Loss/Nakamura/Stolz: Understanding the Random Displacement Model: from Ground-State Properties to Localization.- Ojeda-Valencia/Villegas-Blas: On limiting eigenvalue theorems in semiclassical analysis.- de Oliveira/Verri: On norm resolvent and quadratic form convergences in asymptotic thin spatial waveguides.- Rebolledo: Equilibrium Analysis of a Dissipative Fermion System.- Richard/Tiedra de Aldecoa: A new formula relating localisation operators to time operators
Series: Trends in Mathematics
2013, 2013, 275 p.
Hardcover, ISBN 978-3-0348-0372-4
Due: June 30, 2013
.The book represents current research in concentration and blow-up phenomena from various perspectives, with a variety of applications to elliptic and evolution PDEs, as well as a systematic functional-analytic background for concentration phenomena, presented by profile decompositions based on wavelet theory and cocompact imbeddings.
Content Level ≫ Research
Related subjects ≫ Analysis - Dynamical Systems & Differential Equations
Series: Springer Series in Statistics, Vol. 199
2012, 2012, X, 290 p. 41 illus.
Hardcover, ISBN 978-1-4614-3718-5
Due: June 29, 2012
Crucial guide for statisticians no matter previous exposure to algebra and algebraic statistics
Clear organization guides the reader through the 16 chapters with figures and tables
Shows topic in its broader context, beginning with introductory material
Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra meet and stimulate new research directions. One of the origins of algebraic statistics is the work by Diaconis and Sturmfels in 1998 on the use of Grobner bases for constructing a connected Markov chain for performing conditional tests of a discrete exponential family. In this book we take up this topic and present a detailed summary of developments following the seminal work of Diaconis and Sturmfels.
This book is intended for statisticians with minimal backgrounds in algebra. As we ourselves learned algebraic notions through working on statistical problems and collaborating with notable algebraists, we hope that this book with many practical statistical problems is useful for statisticians to start working on the field.
Satoshi Aoki obtained his doctoral degree from University of Tokyo in 2004 and is currently an associate professor in Graduate school of Science and Engineering, Kagoshima University.
Hisayuki Hara obtained his doctoral degree from University of Tokyo in 1999 and is currently an associate professor in Faculty of Economics, Niigata University.
Akimichi Takemura obtained his doctoral degree from Stanford University in 1982 and is currently a professor in Graduate School of Information Science and Technology, University of Tokyo.
Exact tests for contingency tables and discrete exponential families.- Markov chain Monte Carlo methods over discrete sample space.- Toric ideals and their Grobner bases.- Definition of Markov bases and other bases.- Structure of minimal Markov bases.- Method of distance reduction.- Symmetry of Markov bases.- Decomposable models of contingency tables.- Markov basis for no-three-factor interaction models and some other hierarchical models.- Two-way tables with structural zeros and fixed subtable sums.- Regular factorial designs with discrete response variables.- Group-wise selection models.- The set of moves connecting specific fibers.- Disclosure limitation problem and Markov basis.- Grobner basis techniques for design of experiments.- Running Markov chain without Markov bases.- References.- Index.
2012, 2012, X, 200 p.
Hardcover, ISBN 978-0-8176-8327-6
Due: June 2012
Modern approach to operators acting on Hilbert space
Presentation of recent theoretical aspects (including very current research results)
Detailed proofs, including discussions and explanations of delicate points and highlighting some commonly hidden features
Includes chapter and section summaries as well as periodic exercises to enhance pedagogical impact ?
This work is intended to provide a concise introduction to spectral theory of Hilbert space operators. With an emphasis on recent aspects of theory and detailed proofs, it can serve as a modern textbook for a first graduate course in the subject. The coverage of topics is thorough, exploring various intricate points and hidden features often left untreated.
The book begins with a primer on Hilbert space theory, summarizing the basics required for the remainder of the book and establishing unified notation and terminology. After this, standard spectral results for (bounded linear) operators on Banach and Hilbert spaces, including the classical partition of the spectrum and spectral properties for specific classes of operators, are discussed. A study of the spectral theorem for normal operators follows, covering both the compact and the general case, and proving both versions of the theorem in full detail. This leads into an investigation of functional calculus for normal operators and Riesz functional calculus, which in turn is followed by Fredholm theory and compact perturbations of the spectrum, where a finer analysis of the spectrum is worked out. Here, further partitions involving the essential spectrum, including the Weyl and Browder spectra, are introduced. The final section of the book deals with Weyl's and Browder's theorems and provides a look at very recent results.
Spectral Theory of Operators on Hilbert Space is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will be useful for working mathematicians using spectral theory of Hilbert space operators, as well as for scientists wishing to harness the applications of this theory.
Preface.- Preliminaries.- Spectrum.- Spectral Theorem.- ?Functional Calculus.- Fredholm Theory.- References.- Index.