Pseudodifferential And Singular Integral Operators

Author : Helmut Abels
Publisher : Walter de Gruyter
Page : 233 pages
File Size : 42,6 Mb
Release : 2011-12-23
Category : Mathematics
ISBN : 9783110250312

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Pseudodifferential and Singular Integral Operators by Helmut Abels Pdf

This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. In the first chapters, the necessary material on Fourier transformation and distribution theory is presented. Subsequently the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space is developed. In order to present the deep results on regularity questions for partial differential equations, an introduction to the theory of singular integral operators is given - which is of interest for its own. Moreover, to get a wide range of applications, one chapter is devoted to the modern theory of Besov and Bessel potential spaces. In order to demonstrate some fundamental approaches and the power of the theory, several applications to wellposedness and regularity question for elliptic and parabolic equations are presented throughout the book. The basic notation of functional analysis needed in the book is introduced and summarized in the appendix. The text is comprehensible for students of mathematics and physics with a basic education in analysis.

Author : Solomon G. Mikhlin,Siegfried Prößdorf
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 52,6 Mb
Release : 1987
Category : Mathematics
ISBN : 3540159673

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Singular Integral Operators by Solomon G. Mikhlin,Siegfried Prößdorf Pdf

The present edition differs from the original German one mainly in the following addi tional material: weighted norm inequalities for maximal functions and singular opera tors (§ 12, Chap. XI), polysingular integral operators and pseudo-differential operators (§§ 7, 8, Chap. XII), and spline approximation methods for solving singular integral equations (§ 4, Chap. XVII). Furthermore, we added two subsections on polynomial approximation methods for singular integral equations over an interval or with dis continuous coefficients (Nos. 3.6 and 3.7, Chap. XVII). In many places we incorporated new results which, in the vast majority, are from the last five years after publishing the German edition (note that the references are enlarged by about 150 new titles). S. G. Mikhlin wrote §§ 7, 8, Chap. XII, and the other additions were drawn up by S. Prossdorf. We wish to express our deepest gratitude to Dr. A. Bottcher and Dr. R. Lehmann who together translated the text into English carefully and with remarkable expertise.

Author : François Trèves,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 41,7 Mb
Release : 1985
Category : Mathematics
ISBN : 9780821814697

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Pseudodifferential Operators and Applications by François Trèves,American Mathematical Society Pdf

"Proceedings of the Symposium on Pseudodifferential Operators and Fourier Integral Operators with Applications to Partial Differential Equations held at the University of Notre Dame, Notre Dame, Indiana, April 2-5, 1984"--T.p. verso.

Author : Jean-François Treves
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 50,7 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781468487800

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Introduction to Pseudodifferential and Fourier Integral Operators by Jean-François Treves Pdf

I have tried in this book to describe those aspects of pseudodifferential and Fourier integral operator theory whose usefulness seems proven and which, from the viewpoint of organization and "presentability," appear to have stabilized. Since, in my opinion, the main justification for studying these operators is pragmatic, much attention has been paid to explaining their handling and to giving examples of their use. Thus the theoretical chapters usually begin with a section in which the construction of special solutions of linear partial differential equations is carried out, constructions from which the subsequent theory has emerged and which continue to motivate it: parametrices of elliptic equations in Chapter I (introducing pseudodifferen tial operators of type 1, 0, which here are called standard), of hypoelliptic equations in Chapter IV (devoted to pseudodifferential operators of type p, 8), fundamental solutions of strongly hyperbolic Cauchy problems in Chap ter VI (which introduces, from a "naive" standpoint, Fourier integral operators), and of certain nonhyperbolic forward Cauchy problems in Chapter X (Fourier integral operators with complex phase). Several chapters-II, III, IX, XI, and XII-are devoted entirely to applications. Chapter II provides all the facts about pseudodifferential operators needed in the proof of the Atiyah-Singer index theorem, then goes on to present part of the results of A. Calderon on uniqueness in the Cauchy problem, and ends with a new proof (due to J. J. Kohn) of the celebrated sum-of-squares theorem of L. Hormander, a proof that beautifully demon strates the advantages of using pseudodifferential operators.

Author : Alexander Nagel,Elias M. Stein
Publisher : Princeton University Press
Page : 167 pages
File Size : 41,5 Mb
Release : 2015-03-08
Category : Mathematics
ISBN : 9781400870486

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Lectures on Pseudo-Differential Operators by Alexander Nagel,Elias M. Stein Pdf

The theory of pseudo-differential operators (which originated as singular integral operators) was largely influenced by its application to function theory in one complex variable and regularity properties of solutions of elliptic partial differential equations. Given here is an exposition of some new classes of pseudo-differential operators relevant to several complex variables and certain non-elliptic problems. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : S. G. Mikhlin,S. Prössdorf
Publisher : Walter de Gruyter GmbH & Co KG
Page : 528 pages
File Size : 47,6 Mb
Release : 1986-12-31
Category : Mathematics
ISBN : 9783112719152

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Singular Integral Operators by S. G. Mikhlin,S. Prössdorf Pdf

Keine ausführliche Beschreibung für "Singular Integral Operators" verfügbar.

Author : Michael Eugene Taylor
Publisher : Princeton University Press
Page : 464 pages
File Size : 42,6 Mb
Release : 2017-03-14
Category : Mathematics
ISBN : 9781400886104

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Pseudodifferential Operators (PMS-34) by Michael Eugene Taylor Pdf

Here Michael Taylor develops pseudodifferential operators as a tool for treating problems in linear partial differential equations, including existence, uniqueness, and estimates of smoothness, as well as other qualitative properties. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : François Trèves
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 40,5 Mb
Release : 1980
Category : Fourier integral operators
ISBN : 0306404044

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Introduction to Pseudodifferential and Fourier Integral Operators Volume 2 by François Trèves Pdf

Author : M. Taylor
Publisher : Springer
Page : 160 pages
File Size : 44,8 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540372660

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Pseudo Differential Operators by M. Taylor Pdf

These notes are based on the lectures given on partial differential equations at the University of Michigan during the winter semester of 1972, with some extensions. The students to whom these lectures were addressed were assumed to have knowledge of elementary functional analysis, the Fourier transform, distribution theory, and Sobolev spaces, and such tools are used without comment. In this monography, we develop one tool, the calculus of pseudo differential operators, and apply it to several of the main problems of partial differential equations.

Author : Lars Hörmander
Publisher : Springer Science & Business Media
Page : 552 pages
File Size : 40,6 Mb
Release : 1994-12-23
Category : Mathematics
ISBN : 3540138285

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The Analysis of Linear Partial Differential Operators III by Lars Hörmander Pdf

From the reviews: "Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators." L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987. "This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation." J. Brüning in Zentralblatt MATH, 1987.

Author : Jukka Saranen,Gennadi Vainikko
Publisher : Springer Science & Business Media
Page : 461 pages
File Size : 46,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662047965

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Periodic Integral and Pseudodifferential Equations with Numerical Approximation by Jukka Saranen,Gennadi Vainikko Pdf

An attractive book on the intersection of analysis and numerical analysis, deriving classical boundary integral equations arising from the potential theory and acoustics. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.

Author : N. Krupnik
Publisher : Birkhäuser
Page : 212 pages
File Size : 54,7 Mb
Release : 2013-11-22
Category : Science
ISBN : 9783034854634

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Banach Algebras with Symbol and Singular Integral Operators by N. Krupnik Pdf

About fifty years aga S. G. Mikhlin, in solving the regularization problem for two-dimensional singular integral operators [56], assigned to each such operator a func tion which he called a symbol, and showed that regularization is possible if the infimum of the modulus of the symbol is positive. Later, the notion of a symbol was extended to multidimensional singular integral operators (of arbitrary dimension) [57, 58, 21, 22]. Subsequently, the synthesis of singular integral, and differential operators [2, 8, 9]led to the theory of pseudodifferential operators [17, 35] (see also [35(1)-35(17)]*), which are naturally characterized by their symbols. An important role in the construction of symbols for many classes of operators was played by Gelfand's theory of maximal ideals of Banach algebras [201. Using this the ory, criteria were obtained for Fredholmness of one-dimensional singular integral operators with continuous coefficients [34 (42)], Wiener-Hopf operators [37], and multidimensional singular integral operators [38 (2)]. The investigation of systems of equations involving such operators has led to the notion of matrix symbol [59, 12 (14), 39, 41]. This notion plays an essential role not only for systems, but also for singular integral operators with piecewise-continuous (scalar) coefficients [44 (4)]. At the same time, attempts to introduce a (scalar or matrix) symbol for other algebras have failed.

Author : Louis Nirenberg
Publisher : Springer Science & Business Media
Page : 375 pages
File Size : 40,7 Mb
Release : 2011-06-06
Category : Mathematics
ISBN : 9783642110740

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Pseudo-differential Operators by Louis Nirenberg Pdf

S. Agmon: Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators.- J. Bokobza-Haggiag: Une définition globale des opérateurs pseudo-différentiels sur une variété différentiable.- L. Boutet de Monvel: Pseudo-differential operators and analytic function.- A. Calderon: A priori estimates for singular integral operators.- B.F. Jones: Characterization of spaces of Bessel potentials related to the heat equation.- J.J. Kohn: Pseudo-differential operators and non-elliptic problems.- R.T. Seeley: Topics in pseudo-differential operators.- I.M. E. Shamir: Boundary value problems for elliptic convolution systems.- Singer: Elliptic operators on manifolds.

Author : Michael E. Taylor
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 52,7 Mb
Release : 2000
Category : Differential equations, Partial
ISBN : 9780821843789

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Tools for PDE by Michael E. Taylor Pdf

Developing three related tools that are useful in the analysis of partial differential equations (PDEs) arising from the classical study of singular integral operators, this text considers pseudodifferential operators, paradifferential operators, and layer potentials.

Author : Alexander Nagel,Fulvio Ricci,Elias M. Stein,Stephen Wainger
Publisher : American Mathematical Soc.
Page : 141 pages
File Size : 44,7 Mb
Release : 2019-01-08
Category : Algebra
ISBN : 9781470434380

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Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms by Alexander Nagel,Fulvio Ricci,Elias M. Stein,Stephen Wainger Pdf

The authors study algebras of singular integral operators on R and nilpotent Lie groups that arise when considering the composition of Calderón-Zygmund operators with different homogeneities, such as operators occuring in sub-elliptic problems and those arising in elliptic problems. These algebras are characterized in a number of different but equivalent ways: in terms of kernel estimates and cancellation conditions, in terms of estimates of the symbol, and in terms of decompositions into dyadic sums of dilates of bump functions. The resulting operators are pseudo-local and bounded on for . . While the usual class of Calderón-Zygmund operators is invariant under a one-parameter family of dilations, the operators studied here fall outside this class, and reflect a multi-parameter structure.