Eigenvalues of the Laplacian for Hecke Triangle Groups PDF Download
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Author: Dennis A. Hejhal
Publisher: American Mathematical Soc.
ISBN: 0821825291
Category : Automorphic functions
Languages : en
Pages : 177
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Book Description
Paper I is concerned with computational aspects of the Selberg trace formalism, considering the usual type of eigenfunction and including an analysis of pseudo cusp forms and their residual effects. Paper II examines the modular group PSL (2, [bold]Z), as such groups have both a discrete and continuous spectrum. This paper only examines the discrete side of the spectrum.
Author: Dennis A. Hejhal
Publisher: American Mathematical Soc.
ISBN: 0821825291
Category : Automorphic functions
Languages : en
Pages : 177
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Book Description
Paper I is concerned with computational aspects of the Selberg trace formalism, considering the usual type of eigenfunction and including an analysis of pseudo cusp forms and their residual effects. Paper II examines the modular group PSL (2, [bold]Z), as such groups have both a discrete and continuous spectrum. This paper only examines the discrete side of the spectrum.
Author: Theodore Gerard Faticoni
Publisher: American Mathematical Soc.
ISBN: 9780821825549
Category : Mathematics
Languages : en
Pages : 164
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Book Description
It is the goal of the memoir to develop a functorial transfer of properties between [italic capital]A and [script capital]M[subscript italic capital]E, the category of modules over [italic capital]E, that is more sensitive than the traditional starting point, Hom([italic capital]A, ·). This memoir should be accessible to anyone who has a working knowledge of rings, modules, functors, and categories equivalent to that gained by reading Anderson and Fuller's text "Rings and Categories of Modules."
Author: Igor Frenkel
Publisher: American Mathematical Soc.
ISBN: 0821825550
Category : Mathematics
Languages : en
Pages : 79
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Book Description
The basic definitions and properties of vertex operator algebras, modules, intertwining operators and related concepts are presented, following a fundamental analogy with Lie algebra theory. The first steps in the development of the general theory are taken, and various natural and useful reformulations of the axioms are given. In particular, tensor products of algebras and modules, adjoint vertex operators and contragradient modules, adjoint intertwining operators and fusion rules are studied in greater depth. This paper lays the monodromy-free axiomatic foundation of the general theory of vertex operator algebras, modules and intertwining operators.
Author: André Joyal
Publisher: American Mathematical Soc.
ISBN: 0821823124
Category : Mathematics
Languages : en
Pages : 87
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Book Description
In this paper we compare, in a precise way, the concept of Grothendieck topos to the classical notion of topological space. The comparison takes the form of a two-fold extension of the idea of space.
Author: Leonid Š. Grinblat
Publisher: American Mathematical Soc.
ISBN: 0821825410
Category : Mathematics
Languages : en
Pages : 122
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Book Description
The main results of this work can be formulated in such a way that they will attract a broad spectrum of mathematical interest, but the main audience includes combinatorialists, set-theorists, and topologists. This paper explores a central question: Suppose one is given an at most countable family of algebras of subsets of some fixed set such that, for each algebra, there exits at least one set that is not a member of that algebra. The principal concern is to determine conditions that, if imposed on the algebras, will insure the existence of a set not belonging to any of them.
Author: Nigel John Kalton
Publisher: American Mathematical Soc.
ISBN: 0821825577
Category : Mathematics
Languages : en
Pages : 105
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Book Description
The general problem addressed in this work is to characterize the possible Banach lattice structures that a separable Banach space may have. The basic questions of uniqueness of lattice structure for function spaces have been studied before, but here the approach uses random measure representations for operators in a new way to obtain more powerful conclusions.
Author: Mark Iosifovich Freĭdlin
Publisher: American Mathematical Soc.
ISBN: 0821825860
Category : Mathematics
Languages : en
Pages : 97
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Book Description
Random perturbations of Hamiltonian systems in Euclidean spaces lead to stochastic processes on graphs, and these graphs are defined by the Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a diffusion process on the graph. Its characteristics are expressed through the Hamiltonian and the characteristics of the noise. Freidlin and Wentzell calculate the process on the graph under certain conditions and develop a technique which allows consideration of a number of asymptotic problems. The Dirichlet problem for corresponding elliptic equations with a small parameter are connected with boundary problems on the graph.
Author: Stephen Semmes
Publisher: American Mathematical Soc.
ISBN: 0821825321
Category : Mathematics
Languages : en
Pages : 111
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Book Description
Similar in philosophy to the study of moduli spaces in algebraic geometry, the central theme of this book is that spaces of (pseudoconvex) domains should admit geometrical structures that reflect the complex geometry of the underlying domains in a natural way. With its unusual geometric perspective of some topics in several complex variables, this book appeals to those who view much of mathematics in broadly geometrical terms.
Author: Maria del Rosario Gonzalez-Dorrego
Publisher: American Mathematical Soc.
ISBN: 0821825747
Category : Mathematics
Languages : en
Pages : 114
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Book Description
The philosophy of the first part of this work is to understand (and classify) Kummer surfaces by studying (16, 6) configurations. Chapter 1 is devoted to classifying (16, 6) configurations and studying their manifold symmetries and the underlying questions about finite subgroups of [italic capitals]PGL4([italic]k). In chapter 2 we use this information to give a complete classification of Kummer surfaces together with explicit equations and the explicit description of their singularities.
Author: Stephen Shing-Toung Yau
Publisher: American Mathematical Soc.
ISBN: 0821825674
Category : Mathematics
Languages : en
Pages : 102
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Book Description
In chapter one we address the classification of finite subgroups of [italic capitals]SL([bold]3,[double-struck capital]C). This is followed by a general method to find invariant polynomials and their relations of finite subgroups of [italic capitals]GL([bold]3,[double-struck capital]C). Lastly, we recall some properties of quotient varieties and prove that [double-struck capital]C3/[italic capital]G has isolated singularities if and only if [italic capital]G is abelian and 1 is not an eigenvalue of g in [italic capital]G.
