Hypoelliptic Estimates And Spectral Theory For Fokker Planck Operators And Witten Laplacians
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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.
The Hypoelliptic Laplacian And Ray Singer Metrics
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Author : Jean-Michel Bismut
language : en
Publisher: Princeton University Press
Release Date : 2008-09-07
The Hypoelliptic Laplacian And Ray Singer Metrics written by Jean-Michel Bismut and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-07 with Mathematics categories.
This book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is supposed to interpolate between the classical Laplacian and the geodesic flow. Jean-Michel Bismut and Gilles Lebeau establish the basic functional analytic properties of this operator, which is also studied from the perspective of local index theory and analytic torsion. The book shows that the hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. The authors give the proper functional analytic setting in order to study this operator and develop a pseudodifferential calculus, which provides estimates on the hypoelliptic Laplacian's resolvent. When the deformation parameter tends to zero, the hypoelliptic Laplacian converges to the standard Hodge Laplacian of the base by a collapsing argument in which the fibers of the cotangent bundle collapse to a point. For the local index theory, small time asymptotics for the supertrace of the associated heat kernel are obtained. The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in a key comparison formula between the elliptic and hypoelliptic analytic torsions.
Operator Related Function Theory And Time Frequency Analysis
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Author : Karlheinz Gröchenig
language : en
Publisher: Springer
Release Date : 2014-11-25
Operator Related Function Theory And Time Frequency Analysis written by Karlheinz Gröchenig and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-25 with Mathematics categories.
This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo. The Symposium, and this book, are focused on two important fields of modern mathematical analysis: operator-related function theory and time-frequency analysis; and the profound interplay between them. Among the original contributions and overview lectures gathered here are a paper presenting multifractal analysis as a bridge between geometric measure theory and signal processing; local and global geometry of Prony systems and Fourier reconstruction of piecewise-smooth functions; Bernstein's problem on weighted polynomial approximation; singular distributions and symmetry of the spectrum; and many others. Offering a selection of the latest and most exciting results obtained by world-leading researchers, the book will benefit scientists working in Harmonic and Complex Analysis, Mathematical Physics and Signal Processing.
Tunneling Estimates And Approximate Controllability For Hypoelliptic Equations
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Author : Camille Laurent
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-08
Tunneling Estimates And Approximate Controllability For Hypoelliptic Equations written by Camille Laurent and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-08 with Mathematics categories.
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Advances In Partial Differential Equations And Control
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Author : Kaïs Ammari
language : en
Publisher: Springer Nature
Release Date : 2024-07-27
Advances In Partial Differential Equations And Control written by Kaïs Ammari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-27 with Mathematics categories.
This volume presents a timely overview of control theory and related topics, such as the reconstruction problem, the stability of PDEs, and the Calderón problem. The chapters are based on talks given at the conference "Control & Related Fields” held in Seville, Spain in March 2023. In addition to providing a snapshot of these areas, chapters also highlight breakthroughs on more specific topics, such as: Stabilization of an acoustic system The Kramers-Fokker-Planck operator Control of parabolic equations Control of the wave equation Advances in Partial Differential Equations and Control will be a valuable resource for both established researchers as well as more junior members of the community.
The D Bar Neumann Problem And Schr Dinger Operators
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Author : Friedrich Haslinger
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-08-20
The D Bar Neumann Problem And Schr Dinger Operators written by Friedrich Haslinger and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-20 with Mathematics categories.
The topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations. It begins with results on the canonical solution operator to restricted to Bergman spaces of holomorphic d-bar functions in one and several complex variables.These operators are Hankel operators of special type. In the following the general complex is investigated on d-bar spaces over bounded pseudoconvex domains and on weighted d-bar spaces. The main part is devoted to the spectral analysis of the complex Laplacian and to compactness of the Neumann operator. The last part contains a detailed account of the application of the methods to Schrödinger operators, Pauli and Dirac operators and to Witten-Laplacians. It is assumed that the reader has a basic knowledge of complex analysis, functional analysis and topology. With minimal prerequisites required, this book provides a systematic introduction to an active area of research for both students at a bachelor level and mathematicians.
Control Theory And Inverse Problems
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Author : Kaïs Ammari
language : en
Publisher: Springer Nature
Release Date : 2024-11-07
Control Theory And Inverse Problems written by Kaïs Ammari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-07 with Science categories.
This volume presents a timely overview of control theory and inverse problems, and highlights recent advances in these active research areas. The chapters are based on talks given at the spring school "Control Theory & Inverse Problems” held in Monastir, Tunisia in May 2023. In addition to providing a snapshot of these two areas, chapters also highlight breakthroughs on more specific topics, such as: Control of hyperbolic systems The Helffer-Nier Conjecture Rapid stabilization of the discretized Vlasov system Exponential stability of a delayed thermoelastic system Control Theory and Inverse Problems will be a valuable resource for both established researchers as well as more junior members of the community.
Harmonic Analysis And Partial Differential Equations
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Author : Michael Ruzhansky
language : en
Publisher: Springer Nature
Release Date : 2023-03-06
Harmonic Analysis And Partial Differential Equations written by Michael Ruzhansky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-06 with Mathematics categories.
This book collects papers related to the session “Harmonic Analysis and Partial Differential Equations” held at the 13th International ISAAC Congress in Ghent and provides an overview on recent trends and advances in the interplay between harmonic analysis and partial differential equations. The book can serve as useful source of information for mathematicians, scientists and engineers. The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.
Analysis And Operator Theory
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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2019-05-31
Analysis And Operator Theory written by Themistocles M. Rassias and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-31 with Mathematics categories.
Dedicated to Tosio Kato’s 100th birthday, this book contains research and survey papers on a broad spectrum of methods, theories, and problems in mathematics and mathematical physics. Survey papers and in-depth technical papers emphasize linear and nonlinear analysis, operator theory, partial differential equations, and functional analysis including nonlinear evolution equations, the Korteweg–de Vries equation, the Navier–Stokes equation, and perturbation theory of linear operators. The Kato inequality, the Kato type matrix limit theorem, the Howland–Kato commutator problem, the Kato-class of potentials, and the Trotter–Kato product formulae are discussed and analyzed. Graduate students, research mathematicians, and applied scientists will find that this book provides comprehensive insight into the significance of Tosio Kato’s impact to research in analysis and operator theory.
Asymptotics For Dissipative Nonlinear Equations
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Author : Nakao Hayashi
language : en
Publisher: Springer
Release Date : 2006-08-23
Asymptotics For Dissipative Nonlinear Equations written by Nakao Hayashi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-23 with Mathematics categories.
This is the first book in world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.