Author: Helge Glöckner
Publisher: American Mathematical Soc.
ISBN: 0821832565
Category : Mathematics
Languages : en
Pages : 150
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Book Description
A memoir that studies positive definite functions on convex subsets of finite- or infinite-dimensional vector spaces. It studies representations of convex cones by positive operators on Hilbert spaces. It also studies the interplay between positive definite functions and representations of convex cones.
Author: Helge Glckner
Publisher: American Mathematical Soc.
ISBN: 9780821865118
Category : Mathematics
Languages : en
Pages : 160
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Book Description
This memoir is devoted to the study of positive definite functions on convex subsets of finite- or infinite-dimensional vector spaces, and to the study of representations of convex cones by positive operators on Hilbert spaces. Given a convex subset $\Omega\subseteq V$ of a real vector space $V$, we show that a function $\phi\!:\Omega\to\mathbb{R}$ is the Laplace transform of a positive measure $\mu$ on the algebraic dual space $V^*$ if and only if $\phi$ is continuous along line segments and positive definite. If $V$ is a topological vector space and $\Omega\subseteq V$ an open convex cone, or a convex cone with non-empty interior, we describe sufficient conditions for the existence of a representing measure $\mu$ for $\phi$ on the topological dual space$V'$. The results are used to explore continuity properties of positive definite functions on convex cones, and their holomorphic extendibility to positive definite functions on the associated tubes $\Omega+iV\subseteq V_{\mathbb{C}}$. We also study the interplay between positive definite functions and representations of convex cones, and derive various characterizations of those representations of convex cones on Hilbert spaces which are Laplace transforms of spectral measures. Furthermore, for scalar- or operator-valued positive definite functions which are Laplace transforms, we realize the associated reproducing kernel Hilbert space as an $L^2$-space $L^2(V^*,\mu)$ of vector-valued functions and link the natural translation operators on the reproducing kernel space to multiplication operators on $L^2(V^*,\mu)$, which gives us refined information concerning the norms of these operators.This memoir is devoted to the study of positive definite functions on convex subsets of finite- or infinite-dimensional vector spaces, and to the study of representations of convex cones by positive operators on Hilbert spaces. Given a convex subset $\Omega\subseteq V$ of a real vector space $V$, we show that a function $\phi\!:\Omega\to\mathbb{R}$ is the Laplace transform of a positive measure $\mu$ on the algebraic dual space $V^*$ if and only if $\phi$ is continuous along line segments and positive definite. If $V$ is a topological vector space and $\Omega\subseteq V$ an open convex cone, or a convex cone with non-empty interior, we describe sufficient conditions for the existence of a representing measure $\mu$ for $\phi$ on the topological dual space $V'$. The results are used to explore continuity properties of positive definite functions on convex cones, and their holomorphic extendibility to positive definite functions on the associated tubes $\Omega+iV\subseteq V_\mathbb C$. We also study the interplay between positive definite functions and representations of convex cones, and derive various characterizations of those representations of convex cones on Hilbert spaces which are Laplace transforms of spectral measures. Furthermore, for scalar- or operator-valued positive definite functions which are Laplace transforms, we realize the associated reproducing kernel Hilbert space as an $L^2$-space $L^2(V^*,\mu)$ of vector-valued functions and link the natural translation operators on the reproducing kernel space to multiplication operators on $L^2(V^*,\mu)$, which gives us refined information concerning the norms of these operators.
Author: Jeff Groah
Publisher: American Mathematical Soc.
ISBN: 082183553X
Category : Mathematics
Languages : en
Pages : 98
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Book Description
Demonstrates the consistency of the Einstein equations at the level of shock-waves by proving the existence of shock wave solutions of the spherically symmetric Einstein equations for a perfect fluid, starting from initial density and velocity profiles that are only locally of bounded total variation.
Author: Mihai Ciucu
Publisher: American Mathematical Soc.
ISBN: 082183794X
Category : Mathematics
Languages : en
Pages : 162
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Book Description
Studies the correlation of holes in random lozenge (i.e., unit rhombus) tilings of the triangular lattice. This book analyzes the joint correlation of these triangular holes when their complement is tiled uniformly at random by lozenges.
Author: Nicole Bopp
Publisher: American Mathematical Soc.
ISBN: 0821836234
Category : Mathematics
Languages : en
Pages : 250
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Book Description
Intends to prove a functional equation for a local zeta function attached to the minimal spherical series for a class of real reductive symmetric spaces.
Author: Ken'ichi Ōshika
Publisher: American Mathematical Soc.
ISBN: 0821837729
Category : Mathematics
Languages : en
Pages : 136
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Book Description
Ahlfors conjectured in 1964 that the limit set of every finitely generated Kleinian group either has Lebesgue measure $0$ or is the entire $S^2$. This title intends to prove that this conjecture is true for purely loxodromic Kleinian groups which are algebraic limits of geometrically finite groups.
Author:
Publisher: American Mathematical Soc.
ISBN: 0821834614
Category :
Languages : en
Pages : 146
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Book Description
Author: Greg Hjorth
Publisher: American Mathematical Soc.
ISBN: 0821837710
Category : Mathematics
Languages : en
Pages : 126
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Book Description
Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional rigidity theorems and relative ergodicity results in this context.
Author: Philip L. Bowers
Publisher: American Mathematical Soc.
ISBN: 0821835238
Category : Mathematics
Languages : en
Pages : 118
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Book Description
Introduction Dessins d'enfants Discrete Dessins via circle packing Uniformizing Dessins A menagerie of Dessins d'enfants Computational issues Additional constructions Non-equilateral triangulations The discrete option Appendix: Implementation Bibliography.
Author: Harold G. Dales
Publisher: American Mathematical Soc.
ISBN: 0821837745
Category : Mathematics
Languages : en
Pages : 206
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Book Description
Let $A$ be a Banach algebra, with second dual space $A""$. We propose to study the space $A""$ as a Banach algebra. There are two Banach algebra products on $A""$, denoted by $\,\Box\,$ and $\,\Diamond\,$. The Banach algebra $A$ is Arens regular if the two products $\Box$ and $\Diamond$ coincide on $A""$.
