Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians PDF Download
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Author: Francis Nier
Publisher: Springer Science & Business Media
ISBN: 9783540242000
Category : Mathematics
Languages : en
Pages : 228
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Book Description
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.
Author: Francis Nier
Publisher: Springer Science & Business Media
ISBN: 9783540242000
Category : Mathematics
Languages : en
Pages : 228
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Book Description
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.
Author: Bernard Helffer
Publisher: Cambridge University Press
ISBN: 1139620517
Category : Mathematics
Languages : en
Pages : 263
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Book Description
Bernard Helffer's graduate-level introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schrödinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The later chapters also introduce non self-adjoint operator theory with an emphasis on the role of the pseudospectra. The author's focus on applications, along with exercises and examples, enables readers to connect theory with practice so that they develop a good understanding of how the abstract spectral theory can be applied. The final chapter provides various problems that have been the subject of active research in recent years and will challenge the reader's understanding of the material covered.
Author: Themistocles M. Rassias
Publisher: Springer
ISBN: 3030126617
Category : Mathematics
Languages : en
Pages : 419
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Book Description
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.
Author: Peter Ebenfelt
Publisher: Springer Science & Business Media
ISBN: 3034600097
Category : Mathematics
Languages : en
Pages : 353
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Book Description
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.
Author: Karlheinz Gröchenig
Publisher: Springer
ISBN: 3319085573
Category : Mathematics
Languages : en
Pages : 204
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Book Description
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.
Author: Kaïs Ammari
Publisher: Springer Nature
ISBN: 3031680464
Category :
Languages : en
Pages : 275
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Book Description
Author:
Publisher: Springer Science & Business Media
ISBN: 3540776443
Category :
Languages : en
Pages : 368
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Book Description
Author: Fraydoun Rezakhanlou
Publisher: Springer
ISBN: 3540737057
Category : Mathematics
Languages : en
Pages : 122
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Book Description
Featuring updated versions of two research courses held at the Centre Émile Borel in Paris in 2001, this book describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields. It also discusses four conjectures for the kinetic behavior of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.
Author: Kaïs Ammari
Publisher: Springer Nature
ISBN: 3031622650
Category :
Languages : en
Pages : 250
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Book Description
Author: Friedrich Haslinger
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110417243
Category : Mathematics
Languages : en
Pages : 348
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Book Description
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
