Pseudodifferential Analysis On Conformally Compact Spaces

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Pseudodifferential Analysis On Conformally Compact Spaces

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Author : Robert Lauter
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Pseudodifferential Analysis On Conformally Compact Spaces written by Robert Lauter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

The $0$-calculus on a manifold with boundary is a micro-localization of the Lie algebra of vector fields that vanish at the boundary. It has been used by Mazzeo, Melrose to study the Laplacian of a conformally compact metric.

Motives Quantum Field Theory And Pseudodifferential Operators

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Author : Alan L. Carey
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Motives Quantum Field Theory And Pseudodifferential Operators written by Alan L. Carey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

This volume contains articles related to the conference ``Motives, Quantum Field Theory, and Pseudodifferntial Operators'' held at Boston University in June 2008, with partial support from the Clay Mathematics Institute, Boston University, and the National Science Foundation. There are deep but only partially understood connections between the three conference fields, so this book is intended both to explain the known connections and to offer directions for further research. In keeping with the organization of the conference, this book contains introductory lectures on each of the conference themes and research articles on current topics in these fields. The introductory lectures are suitable for graduate students and new Ph.D.'s in both mathematics and theoretical physics, as well as for senior researchers, since few mathematicians are expert in any two of the conference areas. Among the topics discussed in the introductory lectures are the appearance of multiple zeta values both as periods of motives and in Feynman integral calculations in perturbative QFT, the use of Hopf algebra techniques for renormalization in QFT, and regularized traces of pseudodifferential operators. The motivic interpretation of multiple zeta values points to a fundamental link between motives and QFT, and there are strong parallels between regularized traces and Feynman integral techniques. The research articles cover a range of topics in areas related to the conference themes, including geometric, Hopf algebraic, analytic, motivic and computational aspects of quantum field theory and mirror symmetry. There is no unifying theory of the conference areas at present, so the research articles present the current state of the art pointing towards such a unification.

An Analogue Of A Reductive Algebraic Monoid Whose Unit Group Is A Kac Moody Group

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Author : Claus Mokler
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

An Analogue Of A Reductive Algebraic Monoid Whose Unit Group Is A Kac Moody Group written by Claus Mokler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

By an easy generalization of the Tannaka-Krein reconstruction we associate to the category of admissible representations of the category ${\mathcal O}$ of a Kac-Moody algebra, and its category of admissible duals, a monoid with a coordinate ring. The Kac-Moody group is the Zariski open dense unit group of this monoid. The restriction of the coordinate ring to the Kac-Moody group is the algebra of strongly regular functions introduced by V. Kac and D. Peterson. This monoid has similar structural properties as a reductive algebraic monoid. In particular it is unit regular, its idempotents related to the faces of the Tits cone. It has Bruhat and Birkhoff decompositions. The Kac-Moody algebra is isomorphic to the Lie algebra of this monoid.

Points On Quantum Projectivizations

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Author :
language : en
Publisher: American Mathematical Soc.
Release Date :

Points On Quantum Projectivizations written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Ergodic Theory Of Equivariant Diffeomorphisms Markov Partitions And Stable Ergodicity

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Author : Mike Field
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Ergodic Theory Of Equivariant Diffeomorphisms Markov Partitions And Stable Ergodicity written by Mike Field and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

On the assumption that the $\Gamma$-orbits all have dimension equal to that of $\Gamma$, this title shows that there is a naturally defined $F$- and $\Gamma$-invariant measure $\nu$ of maximal entropy on $\Lambda$ (it is not assumed that the action of $\Gamma$ is free).

Well Posedness For General 2 Times 2 Systems Of Conservation Laws

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Author : Fabio Ancona
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Well Posedness For General 2 Times 2 Systems Of Conservation Laws written by Fabio Ancona and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

Considers the Cauchy problem for a strictly hyperbolic $2\times 2$ system of conservation laws in one space dimension $u_t+ F(u)]_x=0, u(0, x)=\bar u(x), $ which is neither linearly degenerate nor genuinely non-linea

Nonlinear Hyperbolic Equations Spectral Theory And Wavelet Transformations

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Author : Sergio Albeverio
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Nonlinear Hyperbolic Equations Spectral Theory And Wavelet Transformations written by Sergio Albeverio and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This volume focuses on recent developments in non-linear and hyperbolic equations. It will be a most valuable resource for researchers in applied mathematics, the theory of wavelets, and in mathematical and theoretical physics. Nine up-to-date contributions have been written on invitation by experts in the respective fields. The book is the third volume of the subseries "Advances in Partial Differential Equations".

Conformal And Harmonic Measures On Laminations Associated With Rational Maps

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Author : Vadim A. Kaimanovich
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Conformal And Harmonic Measures On Laminations Associated With Rational Maps written by Vadim A. Kaimanovich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

This book is dedicated to Dennis Sullivan on the occasion of his 60th birthday. The framework of affine and hyperbolic laminations provides a unifying foundation for many aspects of conformal dynamics and hyperbolic geometry. The central objects of this approach are an affine Riemann surface lamination $\mathcal A$ and the associated hyperbolic 3-lamination $\mathcal H$ endowed with an action of a discrete group of isomorphisms. This action is properly discontinuous on $\mathcal H$, which allows one to pass to the quotient hyperbolic lamination $\mathcal M$. Our work explores natural ``geometric'' measures on these laminations. We begin with a brief self-contained introduction to the measure theory on laminations by discussing the relationship between leafwise, transverse and global measures. The central themes of our study are: leafwise and transverse ``conformal streams'' on an affine lamination $\mathcal A$ (analogues of the Patterson-Sullivan conformal measures for Kleinian groups), harmonic and invariant measures on the corresponding hyperbolic lamination $\mathcal H$, the ``Anosov--Sinai cocycle'', the corresponding ``basic cohomology class'' on $\mathcal A$ (which provides an obstruction to flatness), and the Busemann cocycle on $\mathcal H$. A number of related geometric objects on laminations -- in particular, the backward and forward Poincare series and the associated critical exponents, the curvature forms and the Euler class, currents and transverse invariant measures, $\lambda$-harmonic functions and the leafwise Brownian motion -- are discussed along the lines. The main examples are provided by the laminations arising from the Kleinian and the rational dynamics. In the former case, $\mathcal M$ is a sublamination of the unit tangent bundle of a hyperbolic 3-manifold, its transversals can be identified with the limit set of the Kleinian group, and we show how the classical theory of Patterson-Sullivan measures can be recast in terms of our general approach. In the latter case, the laminations were recently constructed by Lyubich and Minsky in [LM97]. Assuming that they are locally compact, we construct a transverse $\delta$-conformal stream on $\mathcal A$ and the corresponding $\lambda$-harmonic measure on $\mathcal M$, where $\lambda=\delta(\delta-2)$. We prove that the exponent $\delta$ of the stream does not exceed 2 and that the affine laminations are never flat except for several explicit special cases (rational functions with parabolic Thurston orbifold).

Maximum Principles On Riemannian Manifolds And Applications

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Author : Stefano Pigola
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Maximum Principles On Riemannian Manifolds And Applications written by Stefano Pigola and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

Aims to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity obtained by the authors.

Invariants Of Boundary Link Cobordism

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Author : Desmond Sheiham
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Invariants Of Boundary Link Cobordism written by Desmond Sheiham and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

An $n$-dimensional $\mu$-component boundary link is a codimension $2$ embedding of spheres $L=\sqcup_{\mu}S DEGREESn \subset S DEGREES{n+2}$ such that there exist $\mu$ disjoint oriented embedded $(n+1)$-manifolds which span the components of $L$. This title proceeds to compute the isomorphism class of $C_{