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Completing the Riesz-Dunford Functional Calculus
  • Language: en
  • Pages: 113

Completing the Riesz-Dunford Functional Calculus

Let [script lowercase]f be any analytic function defined in a neighborhood of the non-empty set [italic]E and let [script]S([italic]E) denote the set of all operator having spectrum included in [italic]E. In this paper the closure and interior of the set [script lowercase]f([script]S([italic]E)) [identical equality] {[script lowercase]f([italic]A): [italic]A [set membership] [script]S([italic]E)} are characterized. Some applications serve to illustrate the interplay between the analyticity of the functions and the spectral behavior of the operators.

Semistability of Amalgamated Products and HNN-Extensions
  • Language: en
  • Pages: 98

Semistability of Amalgamated Products and HNN-Extensions

In this work, the authors show that amalgamated products and HNN-extensions of finitely presented semistable at infinity groups are also semistable at infinity. A major step toward determining whether all finitely presented groups are semistable at infinity, this result easily generalizes to finite graphs of groups. The theory of group actions on trees and techniques derived from the proof of Dunwoody's accessibility theorem are key ingredients in this work.

The Subregular Germ of Orbital Integrals
  • Language: en
  • Pages: 161

The Subregular Germ of Orbital Integrals

An integral formula for the subregular germ of a [italic small capital]K-orbital integral is developed. The formula holds for any reductive group over a [italic]p-adic field of characteristic zero. This expression of the subregular germ is obtained by applying Igusa's theory of asymptotic expansions. The integral formula is applied to the question of the transfer of a [italic small capital]K-orbital integral to an endoscopic group. It is shown that the quadratic characters arising in the subregular germs are compatible with the transfer. Details of the transfer are given for the subregular germ of unitary groups.

On the Existence of Feller Semigroups with Boundary Conditions
  • Language: en
  • Pages: 81

On the Existence of Feller Semigroups with Boundary Conditions

This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups with Ventcel' (Wentzell) boundary conditions. This paper considers the non-transversal case and solves from the viewpoint of functional analysis the problem of construction of Feller semigroups for elliptic Waldenfels operators. Intuitively, our result may be stated as follows: One can construct a Feller semigroup corresponding to such a diffusion phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it "dies" at which time it reaches the set where the absorption phenomenon occurs.

Projective Modules over Lie Algebras of Cartan Type
  • Language: en
  • Pages: 97

Projective Modules over Lie Algebras of Cartan Type

This paper investigates the question of linkage and block theory for Lie algebras of Cartan type. The second part of the paper deals mainly with block structure and projective modules of Lies algebras of types W and K.

Current Topics In Analytic Function Theory
  • Language: en
  • Pages: 475

Current Topics In Analytic Function Theory

This volume is a collection of research-and-survey articles by eminent and active workers around the world on the various areas of current research in the theory of analytic functions.Many of these articles emerged essentially from the proceedings of, and various deliberations at, three recent conferences in Japan and Korea: An International Seminar on Current Topics in Univalent Functions and Their Applications which was held in August 1990, in conjunction with the International Congress of Mathematicians at Kyoto, at Kinki University in Osaka; An International Seminar on Univalent Functions, Fractional Calculus, and Their Applications which was held in October 1990 at Fukuoka University; and also the Japan-Korea Symposium on Univalent Functions which was held in January 1991 at Gyeongsang National University in Chinju.

Constant Mean Curvature Immersions of Enneper Type
  • Language: en
  • Pages: 90

Constant Mean Curvature Immersions of Enneper Type

This memoir is devoted to the case of constant mean curvature surfaces immersed in [bold]R3. We reduce this geometrical problem to finding certain integrable solutions to the Gauss equation. Many new and interesting examples are presented, including immersed cylinders in [bold]R3 with embedded Delaunay ends and [italic]n-lobes in the middle, and one-parameter families of immersed constant mean curvature tori in [bold]R3. We examine minimal surfaces in hyperbolic three-space, which is in some ways the most complicated case.

Selberg Trace Formulae and Equidistribution Theorems for Closed Geodesics and Laplace
  • Language: en
  • Pages: 113

Selberg Trace Formulae and Equidistribution Theorems for Closed Geodesics and Laplace

This work is concerned with a pair of dual asymptotics problems on a finite-area hyperbolic surface. The first problem is to determine the distribution of closed geodesics in the unit tangent bundle. The second problem is to determine the distribution of eigenfunctions (in microlocal sense) in the unit tangent bundle.

Contributions to Operator Theory and its Applications
  • Language: en
  • Pages: 528

Contributions to Operator Theory and its Applications

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Vertex Algebras and Integral Bases for the Enveloping Algebras of Affine Lie Algebras
  • Language: en
  • Pages: 113

Vertex Algebras and Integral Bases for the Enveloping Algebras of Affine Lie Algebras

We present a new proof of the identities needed to exhibit an explicit [bold]Z-basis for the universal enveloping algebra associated to an affine Lie algebra. We then use the explicit [bold]Z-bases to extend Borcherds' description, via vertex operator representations, of a [bold]Z-form of the enveloping algebras for the simply-laced affine Lie algebras to the enveloping algebras associated to the unequal root length affine Lie algebras.