Download or read book Tran Moscow Math Soc Vol 24 1971 written by V. I. Averbuh A. Brudnyi V. Egorov and published by American Mathematical Soc.. This book was released on 1974-12-31 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spans several topics, including pseudodifferential operators, pseudodifferential equations, function spaces defined by local approximations, differentiable measures, and $o$-metrizable spaces

Download or read book Sixteen papers on differential equations written by D. M. Galin and published by American Mathematical Soc.. This book was released on 1982-12-31 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Pseudodifferential Operators and Spectral Theory written by M.A. Shubin and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: I had mixed feelings when I thought how I should prepare the book for the second edition. It was clear to me that I had to correct all mistakes and misprints that were found in the book during the life of the first edition. This was easy to do because the mistakes were mostly minor and easy to correct, and the misprints were not many. It was more difficult to decide whether I should update the book (or at least its bibliography) somehow. I decided that it did not need much of an updating. The main value of any good mathematical book is that it teaches its reader some language and some skills. It can not exhaust any substantial topic no matter how hard the author tried. Pseudodifferential operators became a language and a tool of analysis of partial differential equations long ago. Therefore it is meaningless to try to exhaust this topic. Here is an easy proof. As of July 3, 2000, MathSciNet (the database of the American Mathematical Society) in a few seconds found 3695 sources, among them 363 books, during its search for "pseudodifferential operator". (The search also led to finding 963 sources for "pseudo-differential operator" but I was unable to check how much the results ofthese two searches intersected). This means that the corresponding words appear either in the title or in the review published in Mathematical Reviews.

Download or read book Direct and Inverse Problems of Mathematical Physics written by R.P. Gilbert and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of papers presented in the special sessions on "Wave Phenomena and Related Topics", and "Asymptotics and Homogenization" of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997. The ISAAC Congress coincided with a U.S.-Japan Seminar also held at the University of Delaware. The latter was supported by the National Science Foundation through Grant INT -9603029 and the Japan Society for the Promotion of Science through Grant MTCS-134. It was natural that the 'participants of both meetings should interact and consequently several persons attending the Congress also presented papers in the Seminar. The success of the ISAAC Congress and the U.S.-Japan Seminar has led to the ISAAC'99 Congress being held in Fukuoka, Japan during August 1999. Many of the same participants will return to this Seminar. Indeed, it appears that the spirit of the U.S.-Japan Seminar will be continued every second year as part of the ISAAC Congresses. We decided to include with the papers presented in the ISAAC Congress and the U.S.-Japan Seminar several very good papers by colleagues from the former Soviet Union. These participants in the ISAAC Congress attended at their own expense. This volume has the title Direct and Inverse Problems of Mathematical Physics which consists of the papers on scattering theory, coefficient identification, uniqueness and existence theorems, boundary controllability, wave propagation in stratified media, viscous flows, nonlinear acoustics, Sobolev spaces, singularity theory, pseudo differential operators, and semigroup theory.

Download or read book Some Applications of Functional Analysis in Mathematical Physics written by S. L. Sobolev and published by American Mathematical Soc.. This book was released on 2008-04-14 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special problems of functional analysis Variational methods in mathematical physics The theory of hyperbolic partial differential equations Comments Appendix: Methode nouvelle a resoudre le probleme de Cauchy pour les equations lineaires hyperboliques normales Comments on the appendix Bibliography Index

Download or read book Semigroups and Automata written by Uno Kaljulaid and published by IOS Press. This book was released on 2006 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a selection of previously published papers and manuscripts of Uno Kaljulaid, an eminent Estonian algebraist of the last century. The central part of the book is the English translation of Kaljulaid's 1979 Candidate thesis, which originally was typewritten in Russian and manufactured in not so many copies. The thesis is devoted to representation theory in the spirit of his thesis advisor B.I. Plotkin: representations of semigroups and algebras, especially extension to this situation, and application of the notion of triangular product of representations for groups introduced by Plotkin. Through representation theory, Kaljulaid became also interested in automata theory, which at a later phase became his main area of interest. Another field of research concerns combinatorics. Besides being an outstanding and most dedicated mathematician, Uno Kaljulaid was also very much interested in the history of mathematics. In particular, he took a vivid interest in the life and work of the great 19th century Dorpat-Tartu algebraist Th. Molien. Kaljulaid was also very interested in teaching and exposition, or popularization of mathematics. Some of his more popular-scientific papers were published in an Estonian language journal Matemaatika ja Kaasaeg (Mathematics and Our Age). Among them, there is a whole series of papers about algebraic matters, culminating in a brilliant, elementary - although partly rather philosophical - essay devoted to Galois theory. Another such series is his excellent essay of Diophantine Geometry in various installments, followed by his loge to another of his teachers Yu. I. Manin. It is believed that the inclusion of these papers here will make it more interesting for beginners, and perhaps even contribute to attracting young people to mathematics.

Download or read book An Axiomatic Approach to Function Spaces Spectral Synthesis and Luzin Approximation written by Lars Inge Hedberg and published by American Mathematical Soc.. This book was released on 2007 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors define axiomatically a large class of function (or distribution) spaces on $N$-dimensional Euclidean space. The crucial property postulated is the validity of a vector-valued maximal inequality of Fefferman-Stein type. The scales of Besov spaces ($B$-spaces) and Lizorkin-Triebel spaces ($F$-spaces), and as a consequence also Sobolev spaces, and Bessel potential spaces, are included as special cases. The main results of Chapter 1 characterize our spaces by means of local approximations, higher differences, and atomic representations. In Chapters 2 and 3 these results are applied to prove pointwise differentiability outside exceptional sets of zero capacity, an approximation property known as spectral synthesis, a generalization of Whitney's ideal theorem, and approximation theorems of Luzin (Lusin) type.

Download or read book Cauchy Problem for Differential Operators with Double Characteristics written by Tatsuo Nishitani and published by Springer. This book was released on 2017-11-24 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well/ill-posed results related to the Cauchy problem for differential operators with non-effectively hyperbolic double characteristics. Previously scattered over numerous different publications, the results are presented from the viewpoint that the Hamilton map and the geometry of bicharacteristics completely characterizes the well/ill-posedness of the Cauchy problem. A doubly characteristic point of a differential operator P of order m (i.e. one where Pm = dPm = 0) is effectively hyperbolic if the Hamilton map FPm has real non-zero eigen values. When the characteristics are at most double and every double characteristic is effectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms. If there is a non-effectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between −Pμj and Pμj , where iμj are the positive imaginary eigenvalues of FPm . Moreover, if 0 is an eigenvalue of FPm with corresponding 4 × 4 Jordan block, the spectral structure of FPm is insufficient to determine whether the Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly characteristic manifold plays a crucial role.

Download or read book Spectral Theory of Functions and Operators II written by and published by American Mathematical Soc.. This book was released on 1980 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Pseudo Differential Operators Singularities Applications written by Iouri Egorov and published by Birkhäuser. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of lecture notes based on the DMV seminar "Pseudo- Differential Operators, Singularities, Applications" held by the authors in Reisenburg-Günzburg, 12–19 July 1992. The modern theory of elliptic boundary value problems in domains having conical or edge singularities on the boundary as well as the classical theory of elliptic boundary value problems and the original Kondratiev theory are presented. This material forms the foundation for the second part of the book which contains a new construction of pseudo-differential operators with symbols corresponding to the singularities of the boundary of different dimensions. This allows in particular to obtain complete asymptotic expansions of solutions near these singularities.

Download or read book Stochastic Equations and Differential Geometry written by Ya.I. Belopolskaya and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... '; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Download or read book Selfadjoint Operators in Spaces of Functions of Infinitely Many Variables written by I_Uri_ Makarovich Berezanski_ and published by American Mathematical Soc.. This book was released on 1986-12-31 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions in the spectral theory of selfadjoint and normal operators acting in spaces of functions of infinitely many variables are studied in this book, and, in particular, the theory of expansions in generalized eigenfunctions of such operators. Both individual operators and arbitrary commuting families of them are considered. A theory of generalized functions of infinitely many variables is constructed. The circle of questions presented has evolved in recent years, especially in connection with problems in quantum field theory. This book will be useful to mathematicians and physicists interested in the indicated questions, as well as to graduate students and students in advanced university courses.

Download or read book Proceedings of the Steklov Institute of Mathematics written by Matematičeskij Institut Imeni V. A. Steklova and published by Cambridge University Press. This book was released on 1967 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Transactions of the Moscow Mathematical Society for the Year written by and published by . This book was released on 1987 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Harmonic Analysis in Phase Space AM 122 Volume 122 written by Gerald B. Folland and published by Princeton University Press. This book was released on 2016-03-02 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.

Download or read book Nigel J Kalton Selecta written by Fritz Gesztesy and published by Birkhäuser. This book was released on 2016-07-05 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second part of a two volume anthology comprising a selection of 49 articles that illustrate the depth, breadth and scope of Nigel Kalton’s research. Each article is accompanied by comments from an expert on the respective topic, which serves to situate the article in its proper context, to successfully link past, present and hopefully future developments of the theory and to help readers grasp the extent of Kalton’s accomplishments. Kalton’s work represents a bridge to the mathematics of tomorrow, and this book will help readers to cross it. Nigel Kalton (1946-2010) was an extraordinary mathematician who made major contributions to an amazingly diverse range of fields over the course of his career.

Download or read book Geometric Theory of Foliations written by César Camacho and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intuitively, a foliation corresponds to a decomposition of a manifold into a union of connected, disjoint submanifolds of the same dimension, called leaves, which pile up locally like pages of a book. The theory of foliations, as it is known, began with the work of C. Ehresmann and G. Reeb, in the 1940's; however, as Reeb has himself observed, already in the last century P. Painleve saw the necessity of creating a geometric theory (of foliations) in order to better understand the problems in the study of solutions of holomorphic differential equations in the complex field. The development of the theory of foliations was however provoked by the following question about the topology of manifolds proposed by H. Hopf in the 3 1930's: "Does there exist on the Euclidean sphere S a completely integrable vector field, that is, a field X such that X· curl X • 0?" By Frobenius' theorem, this question is equivalent to the following: "Does there exist on the 3 sphere S a two-dimensional foliation?" This question was answered affirmatively by Reeb in his thesis, where he 3 presents an example of a foliation of S with the following characteristics: There exists one compact leaf homeomorphic to the two-dimensional torus, while the other leaves are homeomorphic to two-dimensional planes which accu mulate asymptotically on the compact leaf. Further, the foliation is C"".