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Geometric Aspects of Functional Analysis
  • Language: en
  • Pages: 318
Alice and Bob Meet Banach
  • Language: en
  • Pages: 439

Alice and Bob Meet Banach

The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, high-dimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it es...

Geometric Aspects of Functional Analysis
  • Language: en
  • Pages: 350

Geometric Aspects of Functional Analysis

Continuing the theme of the previous volumes, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of...

Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation
  • Language: en
  • Pages: 146

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

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].

Integrable Hamiltonian Systems on Complex Lie Groups
  • Language: en
  • Pages: 150

Integrable Hamiltonian Systems on Complex Lie Groups

Studies the elastic problems on simply connected manifolds $M_n$ whose orthonormal frame bundle is a Lie group $G$. This title synthesizes ideas from optimal control theory, adapted to variational problems on the principal bundles of Riemannian spaces, and the symplectic geometry of the Lie algebra $\mathfrak{g}, $ of $G$

Martingale Theory in Harmonic Analysis and Banach Spaces
  • Language: en
  • Pages: 238

Martingale Theory in Harmonic Analysis and Banach Spaces

  • Type: Book
  • -
  • Published: 2006-11-17
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  • Publisher: Springer

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The Complete Dimension Theory of Partially Ordered Systems with Equivalence and Orthogonality
  • Language: en
  • Pages: 134

The Complete Dimension Theory of Partially Ordered Systems with Equivalence and Orthogonality

Introduction Partial commutative monoids Continuous dimension scales Espaliers Classes of espaliers Bibliography Index

Invariants of Boundary Link Cobordism
  • Language: en
  • Pages: 128

Invariants of Boundary Link Cobordism

An $n$-dimensional $\mu$-component boundary link is a codimension $2$ embedding of spheres $L=\sqcup_{\mu}S DEGREESn \subset S DEGREES{n+2}$ such that there exist $\mu$ disjoint oriented embedded $(n+1)$-manifolds which span the components of $L$. This title proceeds to compute the isomorphism class of $C_{

Interpolation Theory and Applications
  • Language: en
  • Pages: 370

Interpolation Theory and Applications

This volume contains the Proceedings of the Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel (Miami, FL, 2006). The central topic of this book is interpolation theory in its broadest sense, with special attention to its applications to analysis. The articles include applications to classical analysis, harmonic analysis, partial differential equations, function spaces, image processing, geometry of Banach spaces, and more. This volume emphasizes remarkable connections between several branches of pure and applied analysis. Graduate students and researchers in analysis will find it very useful.

Infinite Dimensional Complex Symplectic Spaces
  • Language: en
  • Pages: 94

Infinite Dimensional Complex Symplectic Spaces

Complex symplectic spaces are non-trivial generalizations of the real symplectic spaces of classical analytical dynamics. This title presents a self-contained investigation of general complex symplectic spaces, and their Lagrangian subspaces, regardless of the finite or infinite dimensionality.