Carleman Estimates and Applications to Uniqueness and Control Theory
  • Language: en
  • Pages: 217

Carleman Estimates and Applications to Uniqueness and Control Theory

The articles in this volume reflect a subsequent development after a scientific meeting entitled Carleman Estimates and Control Theory, held in Cartona in September 1999. The 14 research-level articles, written by experts, focus on new results on Carleman estimates and their applications to uniqueness and controlla bility of partial differential equations and systems. The main topics are unique continuation for elliptic PDEs and systems, con trol theory and inverse problems. New results on strong uniqueness for second or higher order operators are explored in detail in several papers. In the area of control theory. the reader will find applications of Carleman estimates to stabiliza tion, ob...

Evolution Equations
  • Language: en
  • Pages: 587

Evolution Equations

This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems. The three main courses focused primarily on microlocal analysis and spectral and scattering ...

Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity
  • Language: en
  • Pages: 170

Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity

View the abstract.

On Maps from Loop Suspensions to Loop Spaces and the Shuffle Relations on the Cohen Groups
  • Language: en
  • Pages: 78

On Maps from Loop Suspensions to Loop Spaces and the Shuffle Relations on the Cohen Groups

The maps from loop suspensions to loop spaces are investigated using group representations in this article. The shuffle relations on the Cohen groups are given. By using these relations, a universal ring for functorial self maps of double loop spaces of double suspensions is given. Moreover the obstructions to the classical exponent problem in homotopy theory are displayed in the extension groups of the dual of the important symmetric group modules Lie$(n)$, as well as in the top cohomology of the Artin braid groups with coefficients in the top homology of the Artin pure braid groups.

Invariant Representations of $\mathrm {GSp}(2)$ under Tensor Product with a Quadratic Character
  • Language: en
  • Pages: 185

Invariant Representations of $\mathrm {GSp}(2)$ under Tensor Product with a Quadratic Character

"Volume 204, number 957 (first of 5 numbers)."

Quasi-Ordinary Power Series and Their Zeta Functions
  • Language: en
  • Pages: 98

Quasi-Ordinary Power Series and Their Zeta Functions

Intends 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, this title computes the local Denef-Loeser motivic zeta function $Z_{\text{DL}}(h, T)$ of a quasi-ordinary power series $h$ of arbitrary dimension

A Categorical Approach to Imprimitivity Theorems for $C^*$-Dynamical Systems
  • Language: en
  • Pages: 186

A Categorical Approach to Imprimitivity Theorems for $C^*$-Dynamical Systems

It has become apparent that studying the representation theory and structure of crossed-product C*-algebras requires imprimitivity theorems. This monograph shows that the imprimitivity theorem for reduced algebras, Green's imprimitivity theorem for actions of groups, and Mansfield's imprimitivity theorem for coactions of groups can all be understoo

Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness
  • Language: en
  • Pages: 187

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

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.)

Erdos Space and Homeomorphism Groups of Manifolds
  • Language: en
  • Pages: 76

Erdos Space and Homeomorphism Groups of Manifolds

Let M be either a topological manifold, a Hilbert cube manifold, or a Menger manifold and let D be an arbitrary countable dense subset of M. Consider the topological group H(M,D) which consists of all autohomeomorphisms of M that map D onto itself equipped with the compact-open topology. We present a complete solution to the topological classification problem for H(M,D) as follows. If M is a one-dimensional topological manifold, then we proved in an earlier paper that H(M,D) is homeomorphic to Qω, the countable power of the space of rational numbers. In all other cases we find in this paper that H(M,D) is homeomorphic to the famed Erdős space E E, which consists of the vectors in Hilbert space l2 with rational coordinates. We obtain the second result by developing topological characterizations of Erdős space.

Affine Insertion and Pieri Rules for the Affine Grassmannian
  • Language: en
  • Pages: 103

Affine Insertion and Pieri Rules for the Affine Grassmannian

The authors study combinatorial aspects of the Schubert calculus of the affine Grassmannian ${\rm Gr}$ associated with $SL(n,\mathbb{C})$.Their main results are: Pieri rules for the Schubert bases of $H^*({\rm Gr})$ and $H_*({\rm Gr})$, which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. A new combinatorial definition for $k$-Schur functions, which represent the Schubert basis of $H_*({\rm Gr})$. A combinatorial interpretation of the pairing $H^*({\rm Gr})\times H_*({\rm Gr}) \rightarrow\mathbb Z$ induced by the cap product.