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Harmonic Analysis for Anisotropic Random Walks on Homogeneous Trees

Author : Alessandro Figà-Talamanca

Publisher : American Mathematical Soc.

Page : 86 pages

File Size : 19,61 MB

Release : 1994

Category : Mathematics

ISBN : 0821825941

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Book Description

This work presents a detailed study of the anisotropic series representations of the free product group Z/2Z*...*Z/2Z. These representations are infinite dimensional, irreducible, and unitary and can be divided into principal and complementary series. Anisotropic series representations are interesting because, while they are not restricted from any larger continuous group in which the discrete group is a lattice, they nonetheless share many properties of such restrictions. The results of this work are also valid for nonabelian free groups on finitely many generators.





Tilting in Abelian Categories and Quasitilted Algebras

Author : Dieter Happel

Publisher : American Mathematical Soc.

Page : 103 pages

File Size : 34,15 MB

Release : 1996

Category : Mathematics

ISBN : 0821804448

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Book Description

We generalize tilting with respect to a tilting module of projective dimension at most one for an Artin algebra to tilting with respect to a torsion pair in an Abelian category. Our construction is motivated by the connection between tilting and derived categories. We develop a general theory for such tilting, and are led to a generalization of tilting algebras which we call quasitilted algebras. This class also contains the canonical algebras, and we show that the quasitilted algebras are characterized by having global dimension at most two and each indecomposable module having projective dimension at most one or injective dimension at most one. We also give other characterizations of quasitilted algebras, and give methods for constructing such algebras.



Inverse Nodal Problems: Finding the Potential from Nodal Lines

Author : Ole H. Hald

Publisher : American Mathematical Soc.

Page : 162 pages

File Size : 41,26 MB

Release : 1996

Category : Mathematics

ISBN : 0821804863

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Book Description

In this paper we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We show that the potential is uniquely determined, up to an additive constant, by a subset of the nodal lines of the eigenfunctions. A formula is shown which, when the additive constant is given, yields an approximation to the potential at a dense set of points. We present an estimate for the error made by the formula. A substantial part of this work is the derivation of the asymptotic forms for a rich set of eigenvalues and eigenfunctions for a large set of rectangles.



$C^*$-Algebra Extensions of $C(X)$

Author : Huaxin Lin

Publisher : American Mathematical Soc.

Page : 102 pages

File Size : 29,43 MB

Release : 1995

Category : Mathematics

ISBN : 0821826115

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Book Description

We show that the Weyl-von Neumann theorem for unitaries holds for [lowercase Greek]Sigma-unital [italic capital]A[italic capital]F-algebras and their multiplier algebras.



Canard Cycles and Center Manifolds

Author : Freddy Dumortier

Publisher : American Mathematical Soc.

Page : 117 pages

File Size : 47,60 MB

Release : 1996

Category : Mathematics

ISBN : 082180443X

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Book Description

In this book, the ``canard phenomenon'' occurring in Van der Pol's equation $\epsilon \ddot x+(x^2+x)\dot x+x-a=0$ is studied. For sufficiently small $\epsilon >0$ and for decreasing $a$, the limit cycle created in a Hopf bifurcation at $a = 0$ stays of ``small size'' for a while before it very rapidly changes to ``big size'', representing the typical relaxation oscillation. The authors give a geometric explanation and proof of this phenomenon using foliations by center manifolds and blow-up of unfoldings as essential techniques. The method is general enough to be useful in the study of other singular perturbation problems.



Second-Order Sturm-Liouville Difference Equations and Orthogonal Polynomials

Author : Alouf Jirari

Publisher : American Mathematical Soc.

Page : 154 pages

File Size : 37,72 MB

Release : 1995

Category : Mathematics

ISBN : 082180359X

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Book Description

This memoir presents machinery for analyzing many discrete physical situations, and should be of interest to physicists, engineers, and mathematicians. We develop a theory for regular and singular Sturm-Liouville boundary value problems for difference equations, generalizing many of the known results for differential equations. We discuss the self-adjointness of these problems as well as their abstract spectral resolution in the appropriate [italic capital]L2 setting, and give necessary and sufficient conditions for a second-order difference operator to be self-adjoint and have orthogonal polynomials as eigenfunctions.



Intersection Pairings on Conley Indices

Author : Henry L. Kurland

Publisher : American Mathematical Soc.

Page : 199 pages

File Size : 30,59 MB

Release : 1996

Category : Mathematics

ISBN : 0821804405

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Book Description

This memoir is a careful and detailed study of the intersection pairing in the Conley index. The Conley index associates to an isolated invariant set of a semiflow (with some mild compactness conditions) a homotopy type of a space, constructed to be invariant under perturbations of the flow. The homology of this space is the homology Conley index. For a (two-sided) flow, each isolated invariant set has two indices defined: one for the forward flow, and one for the reverse. In general, there is no relationship between these two indices, but when the flow is on an orientable manifold, the two indices can be related by an intersection pairing. It is this pairing that receives a careful and detailed study in this memoir. Results are then applied to the motivating example of the work: the existence of transition layer behavior for two-point boundary value problems of singularly perturbed systems.



Pseudofunctors on Modules with Zero Dimensional Support

Author : I-Chiau Huang

Publisher : American Mathematical Soc.

Page : 73 pages

File Size : 18,35 MB

Release : 1995

Category : Mathematics

ISBN : 0821826085

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Book Description

Pseudofunctors with values on modules with zero dimensional support are constructed over the formally smooth category and residually finite category. Combining those pseudofunctors, a pseudofunctor over the category whose objects are Noetherian local rings and whose morphisms are local with finitely generated residue field extensions is constructed.



Automorphisms of the Lattice of Recursively Enumerable Sets

Author : Peter Cholak

Publisher : American Mathematical Soc.

Page : 166 pages

File Size : 37,86 MB

Release : 1995

Category : Mathematics

ISBN : 0821826018

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Book Description

A version of Harrington's [capital Greek]Delta3-automorphism technique for the lattice of recursively enumerable sets is introduced and developed by reproving Soare's Extension Theorem. Then this automorphism technique is used to show two technical theorems: the High Extension Theorem I and the High Extension Theorem II. This is a degree-theoretic technique for constructing both automorphisms of the lattice of r.e. sets and isomorphisms between various substructures of the lattice.