Operators and Representation Theory

Operators and Representation Theory

Author: Palle E.T. Jorgensen

Publisher: Courier Dover Publications

Published: 2017-06-21

Total Pages: 307

ISBN-13: 0486815722

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Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.


Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation

Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation

Author: Benoît Mselati

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 146

ISBN-13: 0821835092

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Concerned with the nonnegative solutions of $\Delta u = u^2$ in a bounded and smooth domain in $\mathbb{R}^d$, this title intends to prove that they are uniquely determined by their fine trace on the boundary as defined in [DK98a], answering a major open question of [Dy02].


Equivariant, Almost-Arborescent Representations of Open Simply-Connected 3-Manifolds; A Finiteness Result

Equivariant, Almost-Arborescent Representations of Open Simply-Connected 3-Manifolds; A Finiteness Result

Author: Valentin Poenaru

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 104

ISBN-13: 0821834606

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Shows that at the cost of replacing $V DEGREES3$ by $V_h DEGREES3 = \{V DEGREES3$ with very many holes $\}$, we can always find representations $X DEGREES2 \stackrel {f} {\rightarrow} V DEGREES3$ with $X DEGREES2$ locally finite and almost-arborescent, with $\Psi (f)=\Phi (f)$, and with the ope


Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness

Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness

Author: Lee Klingler

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 187

ISBN-13: 0821837389

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This memoir completes the series of papers beginning with [KL1,KL2], showing that, for a commutative noetherian ring $\Lambda$, either the category of $\Lambda$-modules of finite length has wild representation type or else we can describe the category of finitely generated $\Lambda$-modules, including their direct-sum relations and local-global relations. (There is a possible exception to our results, involving characteristic 2.)


Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance

Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance

Author: Marc Aristide Rieffel

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 106

ISBN-13: 0821835181

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By a quantum metric space we mean a $C DEGREES*$-algebra (or more generally an order-unit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of Gromov-Hausdorff di


The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups

The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups

Author: Martin W. Liebeck

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 242

ISBN-13: 0821834827

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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.


The Complex Monge-Ampere Equation and Pluripotential Theory

The Complex Monge-Ampere Equation and Pluripotential Theory

Author: Sławomir Kołodziej

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 82

ISBN-13: 082183763X

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We collect here results on the existence and stability of weak solutions of complex Monge-Ampere equation proved by applying pluripotential theory methods and obtained in past three decades. First we set the stage introducing basic concepts and theorems of pluripotential theory. Then the Dirichlet problem for the complex Monge-Ampere equation is studied. The main goal is to give possibly detailed description of the nonnegative Borel measures which on the right hand side of the equation give rise to plurisubharmonic solutions satisfying additional requirements such as continuity, boundedness or some weaker ones. In the last part, the methods of pluripotential theory are implemented to prove the existence and stability of weak solutions of the complex Monge-Ampere equation on compact Kahler manifolds. This is a generalization of the Calabi-Yau theorem.