The Analysis of Linear Partial Differential Operators II

Differential Operators with Constant Coefficients

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Author: Lars Hörmander

Publisher: Springer Science & Business Media

ISBN: 9783540225164

Category: Mathematics

Page: 392

View: 7956

Vol. II of Lars Hörmander's 4-volume treatise is mainly devoted to operators with constant coefficients. From the reviews: "...these volumes are excellently written and make for greatly profitable reading. For years to come they will surely be a main reference for anyone wishing to study partial differential operators." Mathematical Reviews

Analytic, Algebraic and Geometric Aspects of Differential Equations

Będlewo, Poland, September 2015

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Author: Galina Filipuk,Yoshishige Haraoka,Sławomir Michalik

Publisher: Birkhäuser

ISBN: 3319528424

Category: Mathematics

Page: 471

View: 6990

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.

Geometric Analysis

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Author: Hubert L. Bray,Greg Galloway,Rafe Mazzeo,Natasa Sesum

Publisher: American Mathematical Soc.

ISBN: 1470423138

Category: Geometric analysis

Page: 456

View: 4131

This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace–Beltrami operators.

Eigenfunctions of the Laplacian on a Riemannian Manifold

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Author: Steve Zelditch

Publisher: American Mathematical Soc.

ISBN: 1470410370

Category: Eigenfunctions

Page: 394

View: 709

Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.

An Introduction to Sparse Stochastic Processes

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Author: Michael Unser,Pouya D. Tafti

Publisher: Cambridge University Press

ISBN: 1107058546

Category: Computers

Page: 384

View: 3180

A detailed guide to sparsity, providing a description of their transform-domain statistics and applying the models to practical algorithms.

Elliptic Functions According to Eisenstein and Kronecker

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Author: Andre Weil

Publisher: Springer Science & Business Media

ISBN: 9783540650362

Category: Mathematics

Page: 94

View: 4077

From the reviews: "As a contribution to the history of mathematics, this is a model of its kind. While adhering to the basic outlook of Eisenstein and Kronecker, it provides new insight into their work in the light of subsequent developments, right up to the present day. […] it also contains some pertinent comments looking into the future." Bulletin of the London Mathematical Society

Partial Differential Equations and Applications

Proceedings of the CIMPA School Held in Lanzhou (2004)

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Author: Xue Ping Wang,Chengkui Zhong

Publisher: N.A

ISBN: 9782856292372

Category: Differential equations, Partial

Page: 331

View: 6828

The analysis of linear partial differential operators

Distribution theory and Fourier analysis

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Author: Lars Hörmander

Publisher: Springer

ISBN: 9783540523437

Category: Mathematics

Page: 440

View: 9519

Due to popular demand this classic presentation of a vast amount on linear partial differential equations by a consummate master of the subject is now available as a study edition. The main change in this new edition is the inclusion of exercises with answers and hints. That is meant to emphasize that this volume can perfectly serve as a general course in modern analysis on a graduate student level and not only as a beginning of a specialised course in partial differential equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of general interest. As in the revised printing of volume II, a number of minor flaws have also been corrected in this edition. Parallely this edition is still available as volume 256 of the Grundlehren der mathematischen Wissenschaften. "... it is the best now available in print. ... All the theorems are there (among them the Schwartz kernel theorem), and all they have ... proofs." Bulletin of the American Mathematical Society#1 "It certainly will be a classic for many years." Zentralblatt für Mathematik#2

Featured Reviews in Mathematical Reviews 1997-1999

With Selected Reviews of Classic Books and Papers from 1940-1969

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Author: Donald G. Babbitt,Jane E. Kister

Publisher: American Mathematical Soc.

ISBN: 9780821896709

Category: Mathematics

Page: 541

View: 9694

This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.

Books in Series

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Author: N.A

Publisher: N.A

ISBN: 9780835221092

Category: Monographic series

Page: 1756

View: 9001

Guide to Reprints

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Author: Albert James Diaz

Publisher: K G Saur Verlag Gmbh & Co

ISBN: 9783598239076

Category: Out-of-print books

Page: 948

View: 9076

The Subject Guide divides works into over 200 subject groups, facilitating targeted searches by the subject fields. Both parts of the Guide to Reprints contain an Index of Persons as Subject providing fast and reliable access to reprints focussing on specific individuals and their work. Each part also comes with an index of publishers and distributors worldwide along with all relevant information.

Elliptic Partial Differential Equations of Second Order

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Author: David Gilbarg,Neil S. Trudinger

Publisher: Springer Science & Business Media

ISBN: 9783540411604

Category: Mathematics

Page: 517

View: 8743

This work aims to be of interest to those who have to work with differential equations and acts either as a reference or as a book to learn from. The authors have made the treatment self-contained.

Distributions and Convolution Equations

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Author: Semen Grigorʹevich Gindikin,Leonid Romanovich Volevich

Publisher: CRC Press

ISBN: 9782881247538

Category: Mathematics

Page: 465

View: 6398

The authors apply the results of many years of their own original research to a systematic presentation of the theory of distributions in this monograph which can also be used as a (very expensive) textbook on the theory of distribution for graduate students. The first part is devoted to the Cauchy problem, while the second part deals with the Wiener-Hopf equation and related topics in the theory of boundary value problems for convolution equations. To make their work more accessible to readers new to this field, the authors restrict initial treatment of problems to the half-line and formulate only principal results, in their simplest form. Special results and possible generalizations are presented as problems and exercises. Annotation copyrighted by Book News, Inc., Portland, OR

Forthcoming Books

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Author: Rose Arny

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 9507

Perturbation Theory for Linear Operators

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Author: Tosio Kato

Publisher: Springer Science & Business Media

ISBN: 364266282X

Category: Mathematics

Page: 623

View: 9692

From the reviews: "[...] An excellent textbook in the theory of linear operators in Banach and Hilbert spaces. It is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory. [...] I can recommend it for any mathematician or physicist interested in this field." Zentralblatt MATH