Classical Microlocal Analysis in the Space of Hyperfunctions
Classical Microlocal Analysis in the Space of Hyperfunctions

Author: Seiichiro Wakabayashi

Publisher: Springer

Published: 2007-05-06

Total Pages: 373

ISBN-13: 3540451617

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The book develops "Classical Microlocal Analysis" in the spaces of hyperfunctions and microfunctions, which makes it possible to apply the methods in the distribution category to the studies on partial differential equations in the hyperfunction category. Here "Classical Microlocal Analysis" means that it does not use "Algebraic Analysis." The main tool in the text is, in some sense, integration by parts. The studies on microlocal uniqueness, analytic hypoellipticity and local solvability are reduced to the problems to derive energy estimates (or a priori estimates). The author assumes basic understanding of theory of pseudodifferential operators in the distribution category.

Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms
Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms

Author: Min Ho Lee

Publisher: Springer Science & Business Media

Published: 2004-05-13

Total Pages: 262

ISBN-13: 9783540219224

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This volume deals with various topics around equivariant holomorphic maps of Hermitian symmetric domains and is intended for specialists in number theory and algebraic geometry. In particular, it contains a comprehensive exposition of mixed automorphic forms that has never yet appeared in book form. The main goal is to explore connections among complex torus bundles, mixed automorphic forms, and Jacobi forms associated to an equivariant holomorphic map. Both number-theoretic and algebro-geometric aspects of such connections and related topics are discussed.

The Art of Random Walks
The Art of Random Walks

Author: Andras Telcs

Publisher: Springer Science & Business Media

Published: 2006-05-17

Total Pages: 194

ISBN-13: 3540330275

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Einstein proved that the mean square displacement of Brownian motion is proportional to time. He also proved that the diffusion constant depends on the mass and on the conductivity (sometimes referred to Einstein’s relation). The main aim of this book is to reveal similar connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity. The author studies the heat diffusion at this general level and discusses the following topics: The multiplicative Einstein relation, Isoperimetric inequalities, Heat kernel estimates Elliptic and parabolic Harnack inequality.

Asymptotics for Dissipative Nonlinear Equations
Asymptotics for Dissipative Nonlinear Equations

Author: Nakao Hayashi

Publisher: Springer Science & Business Media

Published: 2006-04-21

Total Pages: 570

ISBN-13: 3540320598

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Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the 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.

From Hahn-Banach to Monotonicity
From Hahn-Banach to Monotonicity

Author: Stephen Simons

Publisher: Springer Science & Business Media

Published: 2008-02-13

Total Pages: 251

ISBN-13: 1402069189

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This new edition of LNM 1693 aims to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a "big convexification" of the graph of the multifunction and the "minimax technique" for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with the Hahn-Banach theorem and culminates in a survey of current results on monotone multifunctions on a Banach space.

Simplicial Complexes of Graphs
Simplicial Complexes of Graphs

Author: Jakob Jonsson

Publisher: Springer Science & Business Media

Published: 2007-11-15

Total Pages: 376

ISBN-13: 3540758585

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A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory.

In Memoriam Paul-André Meyer - Séminaire de Probabilités XXXIX
In Memoriam Paul-André Meyer - Séminaire de Probabilités XXXIX

Author: Marc Yor

Publisher: Springer

Published: 2006-10-17

Total Pages: 423

ISBN-13: 3540355138

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The 39th volume of Séminaire de Probabilités is a tribute to the memory of Paul André Meyer. His life and achievements are recalled in this book, and tributes are paid by his friends and colleagues. This volume also contains mathematical contributions to classical and quantum stochastic calculus, the theory of processes, martingales and their applications to mathematical finance and Brownian motion. These contributions provide an overview on the current trends of stochastic calculus.

Introduction to Symplectic Dirac Operators
Introduction to Symplectic Dirac Operators

Author: Katharina Habermann

Publisher: Springer

Published: 2006-10-28

Total Pages: 131

ISBN-13: 3540334211

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This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.

Open Quantum Systems II
Open Quantum Systems II

Author: Stéphane Attal

Publisher: Springer

Published: 2006-08-29

Total Pages: 254

ISBN-13: 3540339663

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Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.

Transseries and Real Differential Algebra
Transseries and Real Differential Algebra

Author: Joris van der Hoeven

Publisher: Springer

Published: 2006-10-31

Total Pages: 265

ISBN-13: 354035591X

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Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.