On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions
| Author | : Peter D. T. A. Elliott |
| Publisher | : |
| Total Pages | : 88 |
| Release | : 1994 |
| Genre | : Arithmetic functions |
| ISBN | : 9781470401177 |
On The Correlation Of Multiplicative And The Sum Of Additive Arithmetic Functions
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On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions
| Author | : Peter D. T. A. Elliott |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 102 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 0821825984 |
The correlation of multiplicative arithmetic functions on distinct arithmetic progressions and with values in the complex unit disc, cannot be continually near to its possible maximum unless each function is either very close to or very far from a generalized character. Moreover, under accessible condition the second possibility can be ruled out. As a consequence analogs of the standard limit theorems in probabilistic number theory are obtained with the classical single additive function on the integers replaced by a sum of two additive functions on distinct arithmetic progressions.
The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms
| Author | : Gilles Pisier |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 119 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 082180474X |
In the recently developed duality theory of operator spaces, bounded operators are replaced by 'completely bounded' ones, isomorphism by 'complete isomorphisms' and Banach spaces by 'operator spaces'. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into [italic capital]B([italic capital]H) (with H being Hilbert). One of the main results is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (which we denote by [italic capitals]OH) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces.
Excluding Infinite Clique Minors
| Author | : Neil Robertson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 116 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821804022 |
For each infinite cardinal [lowercase Greek]Kappa, we give a structural characterization of the graphs with no [italic capital]K[subscript lowercase Greek]Kappa minor. We also give such a characterization of the graphs with no "half-grid" minor.
The Index Theorem for Minimal Surfaces of Higher Genus
| Author | : Friedrich Tomi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 90 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821803522 |
In this paper we formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. Our techniques carry over to surfaces with several boundary contours as well as to unoriented surfaces.
Triangular Algebras and Ideals of Nest Algebras
| Author | : John Lindsay Orr |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 65 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821804057 |
Immersive environments such as virtual reality technology makes possible can respond to their audiences, so that each person's experience of the environment is unique. This volume brings together 11 essays along with artists' projects produced at the Banff Centre for the Arts in Canada to explore issues raised by the creation of virtual environments. The essays approach the social and cultural implications of cyberspace from the perspective of cultural studies, communications, art history, art criticism, English, and women's studies; while artists who created nine virtual worlds at the Banff Centre discuss what they have tried to accomplish in both theoretical and technical terms. With 64 illustrations, including 18 color plates. Annotation copyright by Book News, Inc., Portland, OR
Classification of Direct Limits of Even Cuntz-Circle Algebras
| Author | : Huaxin Lin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 129 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821804030 |
We prove a classification theorem for purely infinite C∗-algebras that is strong enough to show that the tensor products of two different irrational rotation algebras with the same even Cuntz algebra are isomorphic.
Two-Generator Discrete Subgoups of $PSL(2, R)$
| Author | : Jane Gilman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 221 |
| Release | : 1995 |
| Genre | : Gardening |
| ISBN | : 0821803611 |
The discreteness problem is the problem of determining whether or not a two-generator subgroup of $PSL(2, R)$ is discrete. Historically, papers on this old and subtle problem have been known for their errors and omissions. This book presents the first complete geometric solution to the discreteness problem by building upon cases previously presented by Gilman and Maskit and by developing a theory of triangle group shinglings/tilings of the hyperbolic plane and a theory explaining why the solution must take the form of an algorithm. This work is a thoroughly readable exposition that captures the beauty of the interplay between the algebra and the geometry of the solution.
Textile Systems for Endomorphisms and Automorphisms of the Shift
| Author | : Masakazu Nasu |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 230 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821826069 |
We introduce the notion of a textile system. Using this, we study the dynamical properties of endomorphisms and automorphisms of topological Markov shifts including one-sided ones. The dynamical properties of automorphisms of sofic systems are also studied.
Second-Order Sturm-Liouville Difference Equations and Orthogonal Polynomials
| Author | : Alouf Jirari |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 154 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 082180359X |
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.
