Positive Definite Functions on Infinite-Dimensional Convex Cones
Title | Positive Definite Functions on Infinite-Dimensional Convex Cones PDF eBook |
Author | Helge Glöckner |
Publisher | American Mathematical Soc. |
Pages | 150 |
Release | 2003 |
Genre | Mathematics |
ISBN | 0821832565 |
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.
Positive Definite Functions on Infinite-Dimensional Convex Cones
Title | Positive Definite Functions on Infinite-Dimensional Convex Cones PDF eBook |
Author | Helge Glöckner |
Publisher | |
Pages | 128 |
Release | 2014-09-11 |
Genre | Convex bodies |
ISBN | 9781470403874 |
Part I. Preliminaries and Preparatory Results: Bounded and unbounded operators Cone-valued measures Measures on topological spaces Projective limits of cone-valued measures Holomorphic functions Involutive semigroups and their representations Positive definite kernels and functions $\boldmath{C^*}$-algebras associated with involutive semigroups Integral representations of positive definite functions Convex cones and their faces Examples of convex cones Conelike semigroups: definition and examples Representations of conelike semigroups I Fourier and Laplace transforms Generalized Bochner and Stone Theorems Part II. Main Results: Nussbaum Theorem for open convex cones Positive definite functions on convex cones with non-empty interior Positive definite functions on convex sets Associated Hilbert spaces and representations Nussbaum Theorem for generating convex cones Representations of conelike semigroups II Associated unitary representations Holomorphic extension of unitary representations Holomorphic extension of representations of nuclear groups References Index List of symbols.
Infinite Dimensional Complex Symplectic Spaces
Title | Infinite Dimensional Complex Symplectic Spaces PDF eBook |
Author | William Norrie Everitt |
Publisher | American Mathematical Soc. |
Pages | 94 |
Release | 2004 |
Genre | Mathematics |
ISBN | 0821835459 |
Complex symplectic spaces are non-trivial generalizations of the real symplectic spaces of classical analytical dynamics. This title presents a self-contained investigation of general complex symplectic spaces, and their Lagrangian subspaces, regardless of the finite or infinite dimensionality.
Holomorphy and Convexity in Lie Theory
Title | Holomorphy and Convexity in Lie Theory PDF eBook |
Author | Karl-Hermann Neeb |
Publisher | Walter de Gruyter |
Pages | 804 |
Release | 2011-04-20 |
Genre | Mathematics |
ISBN | 3110808145 |
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups
Title | The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups PDF eBook |
Author | Martin W. Liebeck |
Publisher | American Mathematical Soc. |
Pages | 242 |
Release | 2004 |
Genre | Mathematics |
ISBN | 0821834827 |
Intends to complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This title follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small.
Quasi-Ordinary Power Series and Their Zeta Functions
Title | Quasi-Ordinary Power Series and Their Zeta Functions PDF eBook |
Author | Enrique Artal-Bartolo |
Publisher | American Mathematical Soc. |
Pages | 100 |
Release | 2005-10-05 |
Genre | Functions, Zeta |
ISBN | 9780821865637 |
The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser motivic zeta function $Z_{\text{DL}}(h,T)$ of a quasi-ordinary power series $h$ of arbitrary dimension over an algebraically closed field of characteristic zero from its characteristic exponents without using embedded resolution of singularities. This allows us to effectively represent $Z_{\text{DL}}(h,T)=P(T)/Q(T)$ such that almost all the candidate poles given by $Q(T)$ are poles. Anyway, these candidate poles give eigenvalues of the monodromy action on the complex $R\psi_h$ of nearby cycles on $h^{-1}(0).$ In particular we prove in this case the monodromy conjecture made by Denef-Loeser for the local motivic zeta function and the local topological zeta function. As a consequence, if $h$ is a quasi-ordinary polynomial defined over a number field we prove the Igusa monodromy conjecture for its local Igusa zeta function.
A Generating Function Approach to the Enumeration of Matrices in Classical Groups over Finite Fields
Title | A Generating Function Approach to the Enumeration of Matrices in Classical Groups over Finite Fields PDF eBook |
Author | Jason Fulman |
Publisher | American Mathematical Soc. |
Pages | 104 |
Release | 2005 |
Genre | Mathematics |
ISBN | 0821837060 |
Generating function techniques are used to study the probability that an element of a classical group defined over a finite field is separable, cyclic, semisimple or regular. The limits of these probabilities as the dimension tends to infinity are calculated in all cases, and exponential convergence to the limit is proved. These results complement and extend earlier results of the authors, G. E. Wall, and Guralnick & Lubeck.