Complexes Of Partial Differential Operators
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Complexes Of Partial Differential Operators
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Author : Aldo Andreotti
language : en
Publisher:
Release Date : 1975
Complexes Of Partial Differential Operators written by Aldo Andreotti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Complexes Of Partial Differential Operators
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Author : Aldo Andreotti
language : en
Publisher:
Release Date :
Complexes Of Partial Differential Operators written by Aldo Andreotti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Complexes Of Partial Differential Operators Volume 6
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Author : A. ANDREOTTI
language : en
Publisher:
Release Date : 1975
Complexes Of Partial Differential Operators Volume 6 written by A. ANDREOTTI and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Complexes Of Differential Operators
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Author : Nikolai Tarkhanov
language : en
Publisher:
Release Date : 2014-01-15
Complexes Of Differential Operators written by Nikolai Tarkhanov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Complexes Of Differential Operators
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Author : Nikolai Tarkhanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Complexes Of Differential Operators written by Nikolai Tarkhanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book gives a systematic account of the facts concerning complexes of differential operators on differentiable manifolds. The central place is occupied by the study of general complexes of differential operators between sections of vector bundles. Although the global situation often contains nothing new as compared with the local one (that is, complexes of partial differential operators on an open subset of ]Rn), the invariant language allows one to simplify the notation and to distinguish better the algebraic nature of some questions. In the last 2 decades within the general theory of complexes of differential operators, the following directions were delineated: 1) the formal theory; 2) the existence theory; 3) the problem of global solvability; 4) overdetermined boundary problems; 5) the generalized Lefschetz theory of fixed points, and 6) the qualitative theory of solutions of overdetermined systems. All of these problems are reflected in this book to some degree. It is superfluous to say that different directions sometimes whimsically intersect. Considerable attention is given to connections and parallels with the theory of functions of several complex variables. One of the reproaches avowed beforehand by the author consists of the shortage of examples. The framework of the book has not permitted their number to be increased significantly. Certain parts of the book consist of results obtained by the author in 1977-1986. They have been presented in seminars in Krasnoyarsk, Moscow, Ekaterinburg, and N ovosi birsk.
Partial Differential Equations In Several Complex Variables
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Author : So-chin Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Partial Differential Equations In Several Complex Variables written by So-chin Chen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the study of Cauchy-Riemann and tangential Cauchy-Riemann operators; this progress greatly influenced the development of PDEs and several complex variables. After the background material in complex analysis is developed in Chapters 1 to 3, thenext three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the \bar\partial-Neumann problem, including Hórmander's L2 existence progress on the globalregularity and irregularity of the \bar\partial-Neumann operators. The second part of the book gives a comprehensive study of the tangential Cauchy-Riemann equations, another important class of equations in several complex variables first studied by Lewy. An up-to-date account of the L2 theory for \bar\partial b operator is given. Explicit integral solution representations are constructed both on the Heisenberg groups and on strictly convex boundaries with estimates in Hölder and L2spaces. Embeddability of abstract CR structures is discussed in detail here for the first time.Titles in this series are co-published with International Press, Cambridge, MA.
Complexes Of Differential Operators
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Author : Nikolaĭ Nikolaevich Tarkhanov
language : en
Publisher: Springer Science & Business Media
Release Date : 1995
Complexes Of Differential Operators written by Nikolaĭ Nikolaevich Tarkhanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
The main topic of this work is the study of general complexes of differential operators between sections of vector bundles. Although the global situation and the local one are often similar in content, the invariant language permits the simplification of the notation and more clearly reveals the algebraic structure of some questions.
Pseudo Differential Operators Partial Differential Equations And Time Frequency Analysis
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Author : Luigi Rodino
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Pseudo Differential Operators Partial Differential Equations And Time Frequency Analysis written by Luigi Rodino and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume is based on lectures given at the workshop on pseudo-differential operators held at the Fields Institute from December 11, 2006 to December 15, 2006. The two main themes of the workshop and hence this volume are partial differential equations and time-frequency analysis. The contents of this volume consist of five mini-courses for graduate students and post-docs, and fifteen papers on related topics. Of particular interest in this volume are the mathematical underpinnings, applications and ramifications of the relatively new Stockwell transform, which is a hybrid of the Gabor transform and the wavelet transform. The twenty papers in this volume reflect modern trends in the development of pseudo-differential operators.
Analytic Partial Differential Equations
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Author : François Treves
language : en
Publisher: Springer Nature
Release Date : 2022-04-26
Analytic Partial Differential Equations written by François Treves and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-26 with Mathematics categories.
This book provides a coherent, self-contained introduction to central topics of Analytic Partial Differential Equations in the natural geometric setting. The main themes are the analysis in phase-space of analytic PDEs and the Fourier–Bros–Iagolnitzer (FBI) transform of distributions and hyperfunctions, with application to existence and regularity questions. The book begins by establishing the fundamental properties of analytic partial differential equations, starting with the Cauchy–Kovalevskaya theorem, before presenting an integrated overview of the approach to hyperfunctions via analytic functionals, first in Euclidean space and, once the geometric background has been laid out, on analytic manifolds. Further topics include the proof of the Lojaciewicz inequality and the division of distributions by analytic functions, a detailed description of the Frobenius and Nagano foliations, and the Hamilton–Jacobi solutions of involutive systems of eikonal equations. The reader then enters the realm of microlocal analysis, through pseudodifferential calculus, introduced at a basic level, followed by Fourier integral operators, including those with complex phase-functions (à la Sjöstrand). This culminates in an in-depth discussion of the existence and regularity of (distribution or hyperfunction) solutions of analytic differential (and later, pseudodifferential) equations of principal type, exemplifying the usefulness of all the concepts and tools previously introduced. The final three chapters touch on the possible extension of the results to systems of over- (or under-) determined systems of these equations—a cornucopia of open problems. This book provides a unified presentation of a wealth of material that was previously restricted to research articles. In contrast to existing monographs, the approach of the book is analytic rather than algebraic, and tools such as sheaf cohomology, stratification theory of analytic varieties and symplectic geometry are used sparingly and introduced as required. The first half of the book is mainly pedagogical in intent, accessible to advanced graduate students and postdocs, while the second, more specialized part is intended as a reference for researchers.
Banach Space Complexes
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Author : C.-G. Ambrozie
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Banach Space Complexes written by C.-G. Ambrozie and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The aim of this work is to initiate a systematic study of those properties of Banach space complexes that are stable under certain perturbations. A Banach space complex is essentially an object of the form 1 op-l oP +1 ... --+ XP- --+ XP --+ XP --+ ... , where p runs a finite or infiniteinterval ofintegers, XP are Banach spaces, and oP : Xp ..... Xp+1 are continuous linear operators such that OPOp-1 = 0 for all indices p. In particular, every continuous linear operator S : X ..... Y, where X, Yare Banach spaces, may be regarded as a complex: O ..... X ~ Y ..... O. The already existing Fredholm theory for linear operators suggested the possibility to extend its concepts and methods to the study of Banach space complexes. The basic stability properties valid for (semi-) Fredholm operators have their counterparts in the more general context of Banach space complexes. We have in mind especially the stability of the index (i.e., the extended Euler characteristic) under small or compact perturbations, but other related stability results can also be successfully extended. Banach (or Hilbert) space complexes have penetrated the functional analysis from at least two apparently disjoint directions. A first direction is related to the multivariable spectral theory in the sense of J. L.