Abelian Galois Cohomology of Reductive Groups
Abelian Galois Cohomology of Reductive Groups

Author: Mikhail Borovoi

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 65

ISBN-13: 0821806505

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In this volume, a new function H 2/ab (K, G) of abelian Galois cohomology is introduced from the category of connected reductive groups G over a field K of characteristic 0 to the category of abelian groups. The abelian Galois cohomology and the abelianization map ab1: H1 (K, G) -- H 2/ab (K, G) are used to give a functorial, almost explicit description of the usual Galois cohomology set H1 (K, G) when K is a number field

Wandering Vectors for Unitary Systems and Orthogonal Wavelets
Wandering Vectors for Unitary Systems and Orthogonal Wavelets

Author: Xingde Dai

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 82

ISBN-13: 0821808001

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Investigates topological and structural properties of the set W(U) of all complete wandering vectors for a system U of unitary operators acting on a Hilbert space. The authors parameterize W(U) in terms of a fixed vector y and the set of all unitary operators which locally commute with U at y. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Higher Initial Ideals of Homogeneous Ideals
Higher Initial Ideals of Homogeneous Ideals

Author: Gunnar Fløystad

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 82

ISBN-13: 0821808532

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Given a homogeneous ideal I and a monomial order, the initials ideal in (I) can be formed. The initial idea gives information about I, but quite a lot of information is also lost. The author remedies this by defining a series of higher initial ideals of a homogenous ideal, and considers the case when I is the homogenous ideal of a curve in P3 and the monomial order is reverse lexicographic. No index. Annotation copyrighted by Book News, Inc., Portland, OR

On Stability and Endoscopic Transfer of Unipotent Orbital Integrals on $p$-adic Symplectic Groups
On Stability and Endoscopic Transfer of Unipotent Orbital Integrals on $p$-adic Symplectic Groups

Author: Magdy Assem

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 119

ISBN-13: 082180765X

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The invariant integrals of spherical functions over certain infinite families of unipotent orbits in symplectic groups over a p-adic field of characteristic zero are explicitly calculated. The results are then put into a conjectural framework that predicts for split classical groups which linear combinations of unipotent orbital integrals are stable distributions. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies
Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies

Author: Wolfgang Bulla

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 97

ISBN-13: 0821808087

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In this work, the authors provide a self-contained discussion of all real-valued quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies of completely integrable evolution equations. The approach utilizes algebro-geometric methods, factorization techniques for finite difference expressions, as well as Miura-type transformations. Detailed spectral theoretic properties of Lax pairs and theta function representations of the solutions are derived. Features: Simple and unified treatment of the topic. Self-contained development. Novel results for the Kac-van Moerbeke hierarchy and its algebro-geometric solutions.

Nonlinear Eigenvalues and Analytic-Hypoellipticity
Nonlinear Eigenvalues and Analytic-Hypoellipticity

Author: Ching-Chau Yu

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 106

ISBN-13: 0821807846

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Explores the failure of analytic-hypoellipticity of two partial differential operators. The operators are sums of squares of real analytic vector fields and satisfy Hormander's condition. By reducing to an ordinary differential operator, the author shows the existence of non-linear eigenvalues, which is used to disprove analytic- hypoellipticity of the original operators. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space
Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space

Author: Peter W. Bates

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 145

ISBN-13: 0821808680

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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