The series is devoted to the publication of high-level monographs and specialized graduate texts which cover classical and modern analysis, partial differential equations with natural connections to geometry and the interplays between these ...

MR1016082 (90i:35260) G. ́Olafsson, S. Zheng, Harmonic analysis related to Schrödinger operators, Contemporary Mathematics 464, AMS, 2008, 213–230. MR2440138 (2010b:42028) El-Maati Ouhabaz, Analysis of heat equations on domains (LMS-31) ...

Author: Andrea R. Nahmod

Publisher: American Mathematical Soc.

ISBN: 9780821869215

Category: Mathematics

Page: 285

View: 598

This volume is based on the AMS Special Session on Harmonic Analysis and Partial Differential Equations and the AMS Special Session on Nonlinear Analysis of Partial Differential Equations, both held March 12-13, 2011, at Georgia Southern University, Statesboro, Georgia, as well as the JAMI Conference on Analysis of PDEs, held March 21-25, 2011, at Johns Hopkins University, Baltimore, Maryland. These conferences all concentrated on problems of current interest in harmonic analysis and PDE, with emphasis on the interaction between them. This volume consists of invited expositions as well as research papers that address prospects of the recent significant development in the field of analysis and PDE. The central topics mainly focused on using Fourier, spectral and geometrical methods to treat wellposedness, scattering and stability problems in PDE, including dispersive type evolution equations, higher-order systems and Sobolev spaces theory that arise in aspects of mathematical physics. The study of all these problems involves state-of-the-art techniques and approaches that have been used and developed in the last decade. The interrelationship between the theory and the tools reflects the richness and deep connections between various subjects in both classical and modern analysis.

J. Bourgain, A remark on Schrödinger Operators, Israel J. Math. 77 (1992), 1–16. . L. Carleson, Some Problems in Harmonic Analysis related to Statistical Mechanics, Euclidean Harmonic Analysis (Proceedings of Seminars Held at the ...

Author: Mischa Cotlar

Publisher: American Mathematical Soc.

ISBN: 9780821803042

Category: Mathematics

Page: 511

View: 182

This book is a collection of papers reflecting the conference held in Caracas, Venezuela, in January 1994 in celebration of Professor Mischa Cotlar's eightieth birthday. Presenting an excellent account of recent advances in harmonic analysis and operator theory and their applications, many of the contributors are world leaders in their fields. The collection covers a broad spectrum of topics, including: wavelet analysis, Haenkel operators, multimeasure theory, the boundary behavior of the Bergman kernel, interpolation theory, and Cotlar's Lemma on almost orthogonality in the context of L[superscript p] spaces and more... The range of topics in this volume promotes cross-pollination among the various fields covered. Such variety makes "Harmonic Analysis and Operator Theory" an inspiration for graduate students interested in this area of study.

Author: Alexey N. KarapetyantsPublish On: 2021-08-31

Kiselev, A., Last, Y., Simon, B.: Modified Prüfer and EFCP transforms and the spectral analysis of one-dimensional Schrödinger operators. Preprint (1998). Caltech-Spring 97 21. Koblitz, N.: p-adic Numbers, p-adic Analysis, ...

Author: Alexey N. Karapetyants

Publisher: Springer Nature

ISBN: 9783030768294

Category: Mathematics

Page: 418

View: 308

This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the second in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University, Rostov-on-Don, Russia. This volume focuses on mathematical methods and applications of probability and statistics in the context of general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multi-parameter objects required when considering operators and objects with variable parameters.

Bérthier, A., On the point spectrum of Schrödinger operators, Ann. Sci. Ecole Norm. Sup., 4** 15 (1982), I-15. 9. Bérthier, A. and Georgescu, V., Sur le proprieté de prolongement unique pour l'operateur de Dirac, C.R. Acad.

Author: Jose Garcia-Cuerva

Publisher: Springer

ISBN: 9783540481348

Category: Mathematics

Page: 214

View: 445

The programme of the Conference at El Escorial included 4 main courses of 3-4 hours. Their content is reflected in the four survey papers in this volume (see above). Also included are the ten 45-minute lectures of a more specialized nature.

E. Balslev, J.M. Combes, Spectral properties of many body Schrödinger operators with dilation analytic ... C.A.Berenstein,R.Gay,Complex Analysis and Special Topics in Harmonic Analysis (Springer Science & Business Media, 2012) 23.

Author: Sergio Albeverio

Publisher: Springer Nature

ISBN: 9783030684907

Category: Mathematics

Page: 294

View: 835

This book gives its readers a unique opportunity to get acquainted with new aspects of the fruitful interactions between Analysis, Geometry, Quantum Mechanics and Number Theory. The present book contains a number of contributions by specialists in these areas as an homage to the memory of the mathematician Erik Balslev and, at the same time, advancing a fascinating interdisciplinary area still full of potential. Erik Balslev has made original and important contributions to several areas of Mathematics and its applications. He belongs to the founders of complex scaling, one of the most important methods in the mathematical and physical study of eigenvalues and resonances of Schrödinger operators, which has been very essential in advancing the solution of fundamental problems in Quantum Mechanics and related areas. He was also a pioneer in making available and developing spectral methods in the study of important problems in Analytic Number Theory.

Author: Themistocles M. RassiasPublish On: 2019-05-31

CIMPA School of Harmonic Analysis. Wuhan (China) (1991) Robert, D.: Comportement asymptotique des valeurs propres d'opérateurs du type Schrödinger à potentiel dégénéré. J. Math. Pures Appl. (9) 61(3), 275–300 (1982), (1983) Rothschild, ...

Author: Themistocles M. Rassias

Publisher: Springer

ISBN: 9783030126612

Category: Mathematics

Page: 416

View: 772

Dedicated to Tosio Kato’s 100th birthday, this book contains research and survey papers on a broad spectrum of methods, theories, and problems in mathematics and mathematical physics. Survey papers and in-depth technical papers emphasize linear and nonlinear analysis, operator theory, partial differential equations, and functional analysis including nonlinear evolution equations, the Korteweg–de Vries equation, the Navier–Stokes equation, and perturbation theory of linear operators. The Kato inequality, the Kato type matrix limit theorem, the Howland–Kato commutator problem, the Kato-class of potentials, and the Trotter–Kato product formulae are discussed and analyzed. Graduate students, research mathematicians, and applied scientists will find that this book provides comprehensive insight into the significance of Tosio Kato’s impact to research in analysis and operator theory.

[152] J. Howland (1989): A Localization Theorem for one-dimensional Schrödinger Operators. Preprint University of Virginia. [153] L. K. Hua (1963): Harmonic analysis of several complex variables in the classical domains.

Author: R. Carmona

Publisher: Springer Science & Business Media

ISBN: 9781461244882

Category: Mathematics

Page: 589

View: 340

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.

... a careful analysis shows that F = ∆−1curlb belongs to BMO, and b = c+ DivF. These conditions combined turn out to be necessary and sufficient for (6.29). In [MV6] applications are given to the magnetic Schrödinger operator M ...

Author: Dorina Mitrea

Publisher: American Mathematical Soc.

ISBN: 9780821844243

Category: Mathematics

Page: 423

View: 675

V. G. Mazya is widely regarded as a truly outstanding mathematician whose work spans 50 years and covers many areas of mathematical analysis. This volume contains a unique collection of papers contributed on the occasion of Mazya's 70th birthday by a distinguished group of experts of international stature in the fields of Harmonic Analysis, Partial Differential Equations, Function Theory, Spectral Analysis, and History of Mathematics, reflecting the state of the art in these areas, in which Mazya himself has made some of his most significant contributions.

Author: Jens Gerlach ChristensenPublish On: 2018-08-27

In Frames and operator theory in analysis and signal processing, 119–135, Contemp. Math., 451, Amer. Math. Soc., Providence, RI, 2008. (65) (with S. Zheng) Harmonic Analysis Related to Schrödinger Operators. xvi ́ GESTUR OLAFSSON'S ...

Author: Jens Gerlach Christensen

Publisher: American Mathematical Soc.

ISBN: 9781470440701

Category: Festschriften

Page: 303

View: 348

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis, in honor of Gestur Ólafsson's 65th birthday, held on January 4, 2017, in Atlanta, Georgia. The articles in this volume provide fresh perspectives on many different directions within harmonic analysis, highlighting the connections between harmonic analysis and the areas of integral geometry, complex analysis, operator algebras, Lie algebras, special functions, and differential operators. The breadth of contributions highlights the diversity of current research in harmonic analysis and shows that it continues to be a vibrant and fruitful field of inquiry.