Analytic Deformations Of The Spectrum Of A Family Of Dirac Operators On An Odd Dimensional Manifold With Boundary
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Analytic Deformations Of The Spectrum Of A Family Of Dirac Operators On An Odd Dimensional Manifold With Boundary
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Author : Paul Kirk
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Analytic Deformations Of The Spectrum Of A Family Of Dirac Operators On An Odd Dimensional Manifold With Boundary written by Paul Kirk 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 1996 with Mathematics categories.
The subject of this memoir is the spectrum of a Dirac-type operator on an odd-dimensional manifold M with boundary and, particularly, how this spectrum varies under an analytic perturbation of the operator. Two types of eigenfunctions are considered: first, those satisfying the ``global boundary conditions'' of Atiyah, Patodi, and Singer and second, those which extend to $L^2$ eigenfunctions on M with an infinite collar attached to its boundary. The unifying idea behind the analysis of these two types of spectra is the notion of certain ``eigenvalue-Lagrangians'' in the symplectic space $L^2(\partial M)$, an idea due to Mrowka and Nicolaescu. By studying the dynamics of these Lagrangians, the authors are able to establish that those portions of the two types of spectra which pass through zero behave in essentially the same way (to first non-vanishing order). In certain cases, this leads to topological algorithms for computing spectral flow.
Families Of Curves In P 3 And Zeuthen S Problem
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Author : Robin Hartshorne
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Families Of Curves In P 3 And Zeuthen S Problem written by Robin Hartshorne 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 1997 with Mathematics categories.
Content Description #"November 1997, volume 130, number 617 (first of 4 numbers)."#On t.p. "P" is blackboard bold.#Includes bibliographical references.
Generalized Symplectic Geometries And The Index Of Families Of Elliptic Problems
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Author : Liviu I. Nicolaescu
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Generalized Symplectic Geometries And The Index Of Families Of Elliptic Problems written by Liviu I. Nicolaescu 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 1997 with Geometry, Differential categories.
In this book, an index theorem is proved for arbitrary families of elliptic boundary value problems for Dirac operators and a surgery formula for the index of a family of Dirac operators on a closed manifold. Also obtained is a very general result on the cobordism invariance of the index of a family. All results are established by first symplectically rephrasing the problems and then using a generalized symplectic reduction technique. This provides a unified approach to all possible parameter spaces and all possible symmetries of a Dirac operator (eigh symmetries in the real case and two in the complex case). This text will also be of interest to those working in geometry and topology.
Spectral Asymptotics On Degenerating Hyperbolic 3 Manifolds
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Author : Józef Dodziuk
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Spectral Asymptotics On Degenerating Hyperbolic 3 Manifolds written by Józef Dodziuk 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 1998 with Asymptotic expansions categories.
In this volume, the authors study asymptotics of the geometry and spectral theory of degenerating sequences of finite volume hyperbolic manifolds of three dimensions. Thurston's hyperbolic surgery theorem assets the existence of non-trivial sequences of finite volume hyperbolic three manifolds which converge to a three manifold with additional cusps. In the geometric aspect of their study, the authors use the convergence of hyperbolic metrics on the thick parts of the manifolds under consideration to investigate convergentce of tubes in the manifolds of the sequence to cusps of the limiting manifold. In the specral theory aspect of the work, they prove convergence of heat kernels. They then define a regualrized heat race associated to any finite volume, complete, hyperbolic three manifold, and study its asymptotic behaviour through degeneration. As an application of the analysis of the regularized heat trace, they study asymptotic behaviours of the spectral zeta function, determinant of the Laplacian, Selberg zeta function, and spectral counting functions through degeneration. The authors' methods are an adaptation to three dimensions of the earlier work of Jorgenson and Lundelius who investigated the asymptotic behaviour of spectral functions on degenerating families of finite area hyperbolic Riemann surfaces.
Maximality Properties In Numerical Semigroups And Applications To One Dimensional Analytically Irreducible Local Domains
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Author : Valentina Barucci
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Maximality Properties In Numerical Semigroups And Applications To One Dimensional Analytically Irreducible Local Domains written by Valentina Barucci 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 1997 with Mathematics categories.
If $k$ is a field, $T$ an analytic indeterminate over $k$, and $n_1, \ldots, n_h$ are natural numbers, then the semigroup ring $A = k[[T^{n_1}, \ldots, T^{n_h}]]$ is a Noetherian local one-dimensional domain whose integral closure, $k[[T]]$, is a finitely generated $A$-module. There is clearly a close connection between $A$ and the numerical semigroup generated by $n_1, \ldots, n_h$. More generally, let $A$ be a Noetherian local domain which is analytically irreducible and one-dimensional (equivalently, whose integral closure $V$ is a DVR and a finitely generated $A$-module). As noted by Kunz in 1970, some algebraic properties of $A$ such as ``Gorenstein'' can be characterized by using the numerical semigroup of $A$ (i.e., the subset of $N$ consisting of all the images of nonzero elements of $A$ under the valuation associated to $V$ ). This book's main purpose is to deepen the semigroup-theoretic approach in studying rings A of the above kind, thereby enlarging the class of applications well beyond semigroup rings. For this reason, Chapter I is devoted to introducing several new semigroup-theoretic properties which are analogous to various classical ring-theoretic concepts. Then, in Chapter II, the earlier material is applied in systematically studying rings $A$ of the above type. As the authors examine the connections between semigroup-theoretic properties and the correspondingly named ring-theoretic properties, there are some perfect characterizations (symmetric $\Leftrightarrow$ Gorenstein; pseudo-symmetric $\Leftrightarrow$ Kunz, a new class of domains of Cohen-Macaulay type 2). However, some of the semigroup properties (such as ``Arf'' and ``maximal embedding dimension'') do not, by themselves, characterize the corresponding ring properties. To forge such characterizations, one also needs to compare the semigroup- and ring-theoretic notions of ``type''. For this reason, the book introduces and extensively uses ``type sequences'' in both the semigroup and the ring contexts.
Existence And Persistence Of Invariant Manifolds For Semiflows In Banach Space
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Author : Peter W. Bates
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Existence And Persistence Of Invariant Manifolds For Semiflows In Banach Space written by Peter W. Bates 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 1998 with Differentiable dynamical systems categories.
Extends the theory for normally hyperbolic invariant manifolds to infinite dimensional dynamical systems in a Banach space, thereby providing tools for the study of PDE's and other infinite dimensional equations of evolution. In the process, the authors establish the existence of center-unstable and center-stable manifolds in a neighborhood of the unperturbed compact manifold. No index. Annotation copyrighted by Book News, Inc., Portland, OR
L Functions For The Orthogonal Group
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Author : David Ginzburg
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
L Functions For The Orthogonal Group written by David Ginzburg 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 1997 with Automorphic functions categories.
In this book, the authors establish global Rankin Selberg integrals which determine the standard [italic capital]L function for the group [italic capitals]GL[subscript italic]r x [italic capital]Gʹ, where [italic capital]Gʹ is an isometry group of a nondegenerate symmetric form. The class of automorphic representations considered here is for any pair [capital Greek]Pi1 [otimes/dyadic/Kronecker/tensor product symbol] [capital Greek]Pi2 where [capital Greek]Pi1 is generic cuspidal for [italic capitals]GL[subscript italic]r([italic capital]A) and [capital Greek]Pi2 is cuspidal for [italic capital]Gʹ([italic capital]A). The construction of these [italic capital]L functions involves the use of certain new "models" of local representations; these models generalize the usual generic models. The authors also computer local unramified factors in a new way using geometric ideas.
Two Classes Of Riemannian Manifolds Whose Geodesic Flows Are Integrable
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Author : Kazuyoshi Kiyohara
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Two Classes Of Riemannian Manifolds Whose Geodesic Flows Are Integrable written by Kazuyoshi Kiyohara 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 1997 with Mathematics categories.
In this work, two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and Kahler-Liouville manifolds respectively. In each case, the author finds several invariants with which they are partly classified. The classification indicates, in particular, that these classes contain many new examples of manifolds with integrable geodesic flow.
Bosonic Construction Of Vertex Operator Para Algebras From Symplectic Affine Kac Moody Algebras
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Author : Michael David Weiner
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Bosonic Construction Of Vertex Operator Para Algebras From Symplectic Affine Kac Moody Algebras written by Michael David Weiner 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 1998 with Kac-Moody algebras categories.
Begins with the bosonic construction of four level -1/2 irreducible representations of the symplectic affine Kac-Moody Lie algebra Cl. The direct sum of two of these is given the structure of a vertex operator algebra (VOA), and the direct sum of the other two is given the structure of a twisted VOA-module. The dissertation includes the bosonic analog of the fermionic construction of a vertex operator superalgebra from the four level 1 irreducible modules of type Dl. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Generalized Minkowski Content Spectrum Of Fractal Drums Fractal Strings And The Riemann Zeta Functions
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Author : Christina Q. He
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Generalized Minkowski Content Spectrum Of Fractal Drums Fractal Strings And The Riemann Zeta Functions written by Christina Q. He 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 1997 with Differential equations, Partial categories.
This memoir provides a detailed study of the effect of non power-like irregularities of (the geometry of) the fractal boundary on the spectrum of "fractal drums" (and especially of "fractal strings"). In this work, the authors extend previous results in this area by using the notionof generalized Minkowski content which is defined through some suitable "gauge functions" other than power functions. (This content is used to measure the irregularity (or "fractality") of the boundary of an open set in R]n by evaluating the volume of its small tubular neighborhoods). In the situation when the power function is not the natural "gauge function", this enables the authors to obtain more precise estimates, with a broader potential range of applications than in previous papers of the second author and his collaborators. This text will also be of interest to those working in mathematical physics.