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Heat Kernels and Dirac Operators

In the first edition of this book, simple proofs of the Atiyah-Singer Index Theorem for Dirac operators on compact Riemannian manifolds and;

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Heat Kernels And Spectral Theory

An advanced monograph on a central topic in the theory of differential equations, Heat Kernels and Spectral Theory investigates the theory;

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Singular Integrals and Fourier Theory on Lipschitz Boundaries

monogenic Fourier multipliers, and Cauchy-Dunford functional calculi of the Dirac operators on;

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Singular Integrals and Fourier Theory on Lipschitz Boundaries

monogenic Fourier multipliers, and Cauchy-Dunford functional calculi of the Dirac operators on Lipschitz curves and surfaces, and the high;

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Dirac Operators Yesterday and Today

This volume represents the proceedings of a summer school and workshop on Dirac operators held at the American University of Beirut in 2001;

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Covariant Schroedinger Semigroups on Riemannian Manifolds

This monograph discusses covariant Schroedinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a;

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Asymptotic Formulae in Spectral Geometry

A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type;

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Index Theory, Eta Forms, and Deligne Cohomology

. In this way he develops an inductive procedure to associate Fredholm operators to Dirac operators on manifolds with corners and develops the;

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The Convolution Transform

. The relation between differential operators and integral transforms is the basic theme of this work, which is geared toward upper-level;

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Complex Analysis and Related Topics

This volume is a collection of research and expository papers on different aspects of complex analysis, including relations to operator;

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Elliptic Operators, Topology, and Asymptotic Methods, Second Edition

, and the index theorem for Dirac-type operators using Getzler's direct method. As a dessert, the final two chapters offer discussion;

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Elliptic Operators, Topology, and Asymptotic Methods

, and the index theorem for Dirac-type operators using Getzler's direct method. As a dessert, the final two chapters offer discussion;

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Relativistic Wave Mechanics

transformations. The second section explores particles of spin one-half in terms of spin operators, the Weyl and Dirac equations, constants of motion;

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Partial Differential Equations: Qualitative Studies of Linear Equations: Pt. 2

differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.;

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Partial Differential Equations: v. 3

differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.;

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Partial Differential Equations II

differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.;

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Partial Differential Equations II

differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.;

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L^p-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets

The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local $T(b)$ theorem and;

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Completeness Theorems and Characteristic Matrix Functions

This monograph presents necessary and sufficient conditions for completeness of the linear span of eigenvectors and generalized;

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Heat Conduction

Heat conduction plays an important role in energy transfer at the macro, micro and nano scales. This book collates research results;

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Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare Conjecture

Focusing on Sobolev inequalities and their applications to analysis on manifolds and Ricci flow, Sobolev Inequalities, Heat Kernels under;

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Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms

The authors study algebras of singular integral operators on $mathbb R^n$ and nilpotent Lie groups that arise when considering the;

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Evolutionary Integral Equations and Applications

of the theory including detailed proofs and its applications to problems from mathematical physics, such as viscoelasticity, heat conduction, and;

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Hypoelliptic Laplacian and Orbital Integrals (AM-177)

are also computed. Estimates on the hypoelliptic heat kernel play a key role in the proofs, and are obtained by combining analytic, geometric;

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London Mathematical Society Lecture Note Series

of pseudodifferential operators and its applications, especially to the Dirac theory of quantum mechanics. The treatment uses 'Leibniz formulas' with integral;

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Statistical Mechanics

Statistical Mechanics; Classical and Quantum Statistics; Maxwell-Boltmann, Bose-Einstein, and Fermi-Dirac Statistics Applications;

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The d-bar Neumann Problem and Schrödinger Operators

Neumann operator. The last part contains a detailed account of the application of the methods to Schroedinger operators, Pauli and Dirac;

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