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

Francis Nier,Bernard Helffer
Hypoelliptic Estimates and Spectral Theory for Fokker Planck Operators and Witten Laplacians Book PDF

Author : Francis Nier,Bernard Helffer
Publisher : Springer
Page : 209 pages
File Size : 52,7 Mb
Release : 2005-01-17
Category : Mathematics
ISBN : 9783540315537

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Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians by Francis Nier,Bernard Helffer Pdf

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.

Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians

Francis Nier,Bernard Helffer
Hypoelliptic Estimates and Spectral Theory for Fokker Planck Operators and Witten Laplacians Book PDF

Author : Francis Nier,Bernard Helffer
Publisher : Springer Science & Business Media
Page : 228 pages
File Size : 45,6 Mb
Release : 2005-02-11
Category : Mathematics
ISBN : 3540242007

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Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians by Francis Nier,Bernard Helffer Pdf

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.

Operator-Related Function Theory and Time-Frequency Analysis

Karlheinz Gröchenig,Yurii Lyubarskii,Kristian Seip
Operator Related Function Theory and Time Frequency Analysis Book PDF

Author : Karlheinz Gröchenig,Yurii Lyubarskii,Kristian Seip
Publisher : Springer
Page : 195 pages
File Size : 50,9 Mb
Release : 2014-11-25
Category : Mathematics
ISBN : 9783319085579

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Operator-Related Function Theory and Time-Frequency Analysis by Karlheinz Gröchenig,Yurii Lyubarskii,Kristian Seip Pdf

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.

The Hypoelliptic Laplacian and Ray-Singer Metrics. (AM-167)

Jean-Michel Bismut,Gilles Lebeau
The Hypoelliptic Laplacian and Ray Singer Metrics AM 167 Book PDF

Author : Jean-Michel Bismut,Gilles Lebeau
Publisher : Princeton University Press
Page : 377 pages
File Size : 45,5 Mb
Release : 2008-09-07
Category : Mathematics
ISBN : 9780691137322

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The Hypoelliptic Laplacian and Ray-Singer Metrics. (AM-167) by Jean-Michel Bismut,Gilles Lebeau Pdf

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.

Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations

Camille Laurent,Matthieu Léautaud
Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations Book PDF

Author : Camille Laurent,Matthieu Léautaud
Publisher : American Mathematical Society
Page : 108 pages
File Size : 44,5 Mb
Release : 2022-04-08
Category : Mathematics
ISBN : 9781470451387

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Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations by Camille Laurent,Matthieu Léautaud Pdf

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Analysis and Operator Theory

Themistocles M. Rassias,Valentin A. Zagrebnov
Analysis and Operator Theory Book PDF

Author : Themistocles M. Rassias,Valentin A. Zagrebnov
Publisher : Springer
Page : 416 pages
File Size : 48,7 Mb
Release : 2019-05-31
Category : Mathematics
ISBN : 9783030126612

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Analysis and Operator Theory by Themistocles M. Rassias,Valentin A. Zagrebnov Pdf

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.

Fokker–Planck–Kolmogorov Equations

Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov
Fokker Planck Kolmogorov Equations Book PDF

Author : Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov
Publisher : American Mathematical Society
Page : 495 pages
File Size : 52,5 Mb
Release : 2022-02-10
Category : Mathematics
ISBN : 9781470470098

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Fokker–Planck–Kolmogorov Equations by Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov Pdf

This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker–Planck–Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

The d-bar Neumann Problem and Schrödinger Operators

Friedrich Haslinger
The d bar Neumann Problem and Schr dinger Operators Book PDF

Author : Friedrich Haslinger
Publisher : Walter de Gruyter GmbH & Co KG
Page : 252 pages
File Size : 47,6 Mb
Release : 2014-08-20
Category : Mathematics
ISBN : 9783110315356

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The d-bar Neumann Problem and Schrödinger Operators by Friedrich Haslinger Pdf

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 ond-bar spaces over bounded pseudoconvex domains and on weightedd-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.

Complex Analysis

Peter Ebenfelt,Norbert Hungerbühler,Joseph J. Kohn,Ngaiming Mok,Emil J. Straube
Complex Analysis Book PDF

Author : Peter Ebenfelt,Norbert Hungerbühler,Joseph J. Kohn,Ngaiming Mok,Emil J. Straube
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 47,6 Mb
Release : 2011-01-30
Category : Mathematics
ISBN : 9783034600095

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Complex Analysis by Peter Ebenfelt,Norbert Hungerbühler,Joseph J. Kohn,Ngaiming Mok,Emil J. Straube Pdf

This volume presents the proceedings of a conference on Several Complex Variables, PDE’s, Geometry, and their interactions held in 2008 at the University of Fribourg, Switzerland, in honor of Linda Rothschild.

Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations

Johannes Sjöstrand
Non Self Adjoint Differential Operators Spectral Asymptotics and Random Perturbations Book PDF

Author : Johannes Sjöstrand
Publisher : Springer
Page : 496 pages
File Size : 47,9 Mb
Release : 2019-05-17
Category : Mathematics
ISBN : 9783030108199

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Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations by Johannes Sjöstrand Pdf

The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book. Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.

Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction

Alberto Parmeggiani
Spectral Theory of Non Commutative Harmonic Oscillators An Introduction Book PDF

Author : Alberto Parmeggiani
Publisher : Springer
Page : 260 pages
File Size : 51,8 Mb
Release : 2010-07-23
Category : Mathematics
ISBN : 9783642119224

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Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction by Alberto Parmeggiani Pdf

This book grew out of a series of lectures given at the Mathematics Department of Kyushu University in the Fall 2006, within the support of the 21st Century COE Program (2003–2007) “Development of Dynamical Mathematics with High Fu- tionality” (Program Leader: prof. Mitsuhiro Nakao). It was initially published as the Kyushu University COE Lecture Note n- ber 8 (COE Lecture Note, 8. Kyushu University, The 21st Century COE Program “DMHF”, Fukuoka, 2008. vi+234 pp.), and in the present form is an extended v- sion of it (in particular, I have added a section dedicated to the Maslov index). The book is intended as a rapid (though not so straightforward) pseudodiff- ential introduction to the spectral theory of certain systems, mainly of the form a +a where the entries of a are homogeneous polynomials of degree 2 in the 2 0 2 n n (x,?)-variables, (x,?)? R×R,and a is a constant matrix, the so-called non- 0 commutative harmonic oscillators, with particular emphasis on a class of systems introduced by M. Wakayama and myself about ten years ago. The class of n- commutative harmonic oscillators is very rich, and many problems are still open, and worth of being pursued.

Complex Analysis

Friedrich Haslinger
Complex Analysis Book PDF

Author : Friedrich Haslinger
Publisher : Walter de Gruyter GmbH & Co KG
Page : 347 pages
File Size : 55,5 Mb
Release : 2017-11-20
Category : Mathematics
ISBN : 9783110417241

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Complex Analysis by Friedrich Haslinger Pdf

In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy‘s integral theorem general versions of Runge‘s approximation theorem and Mittag-Leffler‘s theorem are discussed. The fi rst part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Fréchet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator. Contents Complex numbers and functions Cauchy’s Theorem and Cauchy’s formula Analytic continuation Construction and approximation of holomorphic functions Harmonic functions Several complex variables Bergman spaces The canonical solution operator to Nuclear Fréchet spaces of holomorphic functions The -complex The twisted -complex and Schrödinger operators

Boundary Conditions and Subelliptic Estimates for Geometric Kramers-Fokker-Planck Operators on Manifolds with Boundaries

Francis Nier
Boundary Conditions and Subelliptic Estimates for Geometric Kramers Fokker Planck Operators on Manifolds with Boundaries Book PDF

Author : Francis Nier
Publisher : American Mathematical Soc.
Page : 142 pages
File Size : 52,8 Mb
Release : 2018-03-19
Category : Electronic
ISBN : 9781470428020

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Boundary Conditions and Subelliptic Estimates for Geometric Kramers-Fokker-Planck Operators on Manifolds with Boundaries by Francis Nier Pdf

This article is concerned with the maximal accretive realizations of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup. Admissible boundary conditions cover a wide range of applications for the usual scalar Kramer-Fokker-Planck equation or Bismut's hypoelliptic laplacian.

Hyperbolic Problems and Regularity Questions

Mariarosaria Padula,Luisa Zanghirati
Hyperbolic Problems and Regularity Questions Book PDF

Author : Mariarosaria Padula,Luisa Zanghirati
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 41,7 Mb
Release : 2007-01-21
Category : Mathematics
ISBN : 9783764374518

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Hyperbolic Problems and Regularity Questions by Mariarosaria Padula,Luisa Zanghirati Pdf

This book discusses new challenges in the quickly developing field of hyperbolic problems. Particular emphasis lies on the interaction between nonlinear partial differential equations, functional analysis and applied analysis as well as mechanics. The book originates from a recent conference focusing on hyperbolic problems and regularity questions. It is intended for researchers in functional analysis, PDE, fluid dynamics and differential geometry.

Harmonic Analysis and Partial Differential Equations

Michael Ruzhansky,Jens Wirth
Harmonic Analysis and Partial Differential Equations Book PDF

Author : Michael Ruzhansky,Jens Wirth
Publisher : Springer Nature
Page : 241 pages
File Size : 49,6 Mb
Release : 2023-03-06
Category : Mathematics
ISBN : 9783031243110

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Harmonic Analysis and Partial Differential Equations by Michael Ruzhansky,Jens Wirth Pdf

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.