The Local Solvability of Partial Differential Operators on R3 Defined by Heisenberg Group Operators
Author: Christopher James Winfield
Publisher:
Published: 1996
Total Pages: 162
ISBN-13:
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Author: Christopher James Winfield
Publisher:
Published: 1996
Total Pages: 162
ISBN-13:
DOWNLOAD EBOOKAuthor: Daryl Geller
Publisher: Princeton University Press
Published: 2014-07-14
Total Pages: 504
ISBN-13: 1400860733
DOWNLOAD EBOOKMany of the operators one meets in several complex variables, such as the famous Lewy operator, are not locally solvable. Nevertheless, such an operator L can be thoroughly studied if one can find a suitable relative parametrix--an operator K such that LK is essentially the orthogonal projection onto the range of L. The analysis is by far most decisive if one is able to work in the real analytic, as opposed to the smooth, setting. With this motivation, the author develops an analytic calculus for the Heisenberg group. Features include: simple, explicit formulae for products and adjoints; simple representation-theoretic conditions, analogous to ellipticity, for finding parametrices in the calculus; invariance under analytic contact transformations; regularity with respect to non-isotropic Sobolev and Lipschitz spaces; and preservation of local analyticity. The calculus is suitable for doing analysis on real analytic strictly pseudoconvex CR manifolds. In this context, the main new application is a proof that the Szego projection preserves local analyticity, even in the three-dimensional setting. Relative analytic parametrices are also constructed for the adjoint of the tangential Cauchy-Riemann operator. Originally published in 1990. 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: Luigi Rodino
Publisher: World Scientific
Published: 1993-03-30
Total Pages: 266
ISBN-13: 9814505870
DOWNLOAD EBOOKThe book is devoted to new and classical results of the theory of linear partial differential operators in Gevrey spaces. The “microlocal approach” is adopted, by using pseudo-differential operators, wave front sets and Fourier integral operators.Basic results for Schwartz-distributions, c∞ and analytic classes are also included, concerning hypoellipticity, solvability and propagation of singularities.Also included is a self-contained exposition of the calculus of the pseudo-differential operators of infinite order.
Author: Jose Garcia-Cuerva
Publisher: CRC Press
Published: 2018-01-18
Total Pages: 336
ISBN-13: 135108058X
DOWNLOAD EBOOKContains easy access to four actual and active areas of research in Fourier Analysis and PDE Covers a wide spectrum of topics in present research Provides a complete picture of state-of-the-art methods in the field Contains 200 tables allowing the reader speedy access to precise data
Author: Gerald B. Folland
Publisher: Princeton University Press
Published: 2020-05-05
Total Pages: 340
ISBN-13: 0691213038
DOWNLOAD EBOOKThe second edition of Introduction to Partial Differential Equations, which originally appeared in the Princeton series Mathematical Notes, serves as a text for mathematics students at the intermediate graduate level. The goal is to acquaint readers with the fundamental classical results of partial differential equations and to guide them into some aspects of the modern theory to the point where they will be equipped to read advanced treatises and research papers. This book includes many more exercises than the first edition, offers a new chapter on pseudodifferential operators, and contains additional material throughout. The first five chapters of the book deal with classical theory: first-order equations, local existence theorems, and an extensive discussion of the fundamental differential equations of mathematical physics. The techniques of modern analysis, such as distributions and Hilbert spaces, are used wherever appropriate to illuminate these long-studied topics. The last three chapters introduce the modern theory: Sobolev spaces, elliptic boundary value problems, and pseudodifferential operators.
Author: J. Tervo
Publisher:
Published: 1987
Total Pages: 28
ISBN-13:
DOWNLOAD EBOOKAuthor: Lars Hörmander
Publisher: Springer
Published: 2005-12-12
Total Pages: 404
ISBN-13: 3540269649
DOWNLOAD EBOOKAuthor received the 1962 Fields Medal Author received the 1988 Wolf Prize (honoring achievemnets of a lifetime) Author is leading expert in partial differential equations
Author: Al Boggess
Publisher: CRC Press
Published: 1991-09-12
Total Pages: 386
ISBN-13: 9780849371523
DOWNLOAD EBOOKCR Manifolds and the Tangential Cauchy Riemann Complex provides an elementary introduction to CR manifolds and the tangential Cauchy-Riemann Complex and presents some of the most important recent developments in the field. The first half of the book covers the basic definitions and background material concerning CR manifolds, CR functions, the tangential Cauchy-Riemann Complex and the Levi form. The second half of the book is devoted to two significant areas of current research. The first area is the holomorphic extension of CR functions. Both the analytic disc approach and the Fourier transform approach to this problem are presented. The second area of research is the integral kernal approach to the solvability of the tangential Cauchy-Riemann Complex. CR Manifolds and the Tangential Cauchy Riemann Complex will interest students and researchers in the field of several complex variable and partial differential equations.
Author: Nho H o Dinh
Publisher: World Scientific
Published: 1994
Total Pages: 252
ISBN-13: 9789810216115
DOWNLOAD EBOOKThis book is devoted to the theory of infinite-order linear and nonlinear differential operators with several real arguments and their applications to problems of partial differential equations and numerical analysis.Part I develops the theory of pseudodifferential operators with real analytic symbols, the local representatives of which are linear differential operators of infinite order acting in the spaces of basic and generalized functions based on the duality of the spaces of real analytic functions and functionals. Applications to a variety of problems of PDEs and numerical analysis are given. Part II is devoted to the theory of Sobolev-Orlicz spaces of infinite order and the solvability of nonlinear partial differential equations with arbitrary nonlinearities.
Author: Martin Schechter
Publisher: North Holland
Published: 1986
Total Pages: 328
ISBN-13:
DOWNLOAD EBOOKNew material, improvements and recent advances have been added to this second revised edition. The volume examines the general theory for constant coefficient operators, elliptic operators, the L 2 theory for operators bounded from below, and self-adjoint operators. A comprehensive theory for second order operators is given, and applied to quantum mechanical systems of particles. Since many of the topics treated here are of interest to chemists, engineers, mathematicians and physicists, the volume begins with background and reference material.