Solvability Of A Model In The Theory Of Complexes Of Pseudodifferential Operators

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Solvability Of A Model In The Theory Of Complexes Of Pseudodifferential Operators

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Author : Francois Treves
language : en
Publisher:
Release Date : 1977

Solvability Of A Model In The Theory Of Complexes Of Pseudodifferential Operators written by Francois Treves and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Differential equations, Linear 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.

Geometric Analysis Of Pdes And Several Complex Variables

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Author : Shiferaw Berhanu
language : en
Publisher: Springer Nature
Release Date : 2024-10-26

Geometric Analysis Of Pdes And Several Complex Variables written by Shiferaw Berhanu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-26 with Mathematics categories.

This volume convenes selected, peer-reviewed papers presented at the international workshop dedicated to Dr. Jorge Hounie on the occasion of his 75th birthday, held in Serra Negra, Brazil, from July 31 to August 4, 2023. The papers in this volume cover areas that include several complex variables, Cauchy-Riemann geometry, and partial differential equations. An Emeritus at the Federal University of São Carlos (UFScar), Brazil, Dr. Hounie has made significant contributions to partial differential equations, complex variables, harmonic analysis, and involutive structures. He has also been a kind and great mentor to numerous graduate students and postdocs who have gone on to pursue successful academic careers. Born in Bahia Blanca, Argentina, he completed his PhD studies at Rutgers University in 1974 and joined UFSCar as a Full Professor in 1995. He is a Full Member of the Brazilian Academy of Sciences. Within this book, readers will encounter a collection of cutting-edge research papers reflecting Dr. Hounie's research interests, valuable for both experienced researchers and graduate students alike.

Several Complex Variables And Complex Geometry Part Iii

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Author : Eric Bedford
language : en
Publisher: American Mathematical Soc.
Release Date : 1991

Several Complex Variables And Complex Geometry Part Iii written by Eric Bedford 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 1991 with Mathematics categories.

Proceedings Of The American Mathematical Society

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Author : American Mathematical Society
language : en
Publisher:
Release Date : 1977

Proceedings Of The American Mathematical Society written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Electronic journals categories.

Contains the material formerly published in even-numbered issues of the Bulletin of the American Mathematical Society.

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.

Hypoelliptic Estimates And Spectral Theory For Fokker Planck Operators And Witten Laplacians

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Author : Francis Nier
language : en
Publisher: Springer
Release Date : 2005-01-17

Hypoelliptic Estimates And Spectral Theory For Fokker Planck Operators And Witten Laplacians written by Francis Nier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-17 with Mathematics categories.

There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations, and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction, this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart, the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators, the Witten complexes, and the Morse inequalities.

Journal Of The Korean Mathematical Society

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Author :
language : en
Publisher:
Release Date : 1987

Journal Of The Korean Mathematical Society written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.

Annals Of Mathematics

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Author :
language : en
Publisher:
Release Date : 1976

Annals Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Electronic journals categories.

Founded in 1884, Annals of Mathematics publishes research papers in pure mathematics.

Atas Do D Cimo Segundo Col Quio Brasileiro De Matem Tica

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Author :
language : en
Publisher:
Release Date : 1981

Atas Do D Cimo Segundo Col Quio Brasileiro De Matem Tica written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.