Geometric Aspects of Functional Analysis c - Klartag, Bo'az.; Mendelson, Shahar; Milman, Vitali D.; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012)
This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) from the years 2006 to 2011 continues the long tradition of the previous volumes, which reflect the general trends of Asymptotic Geometric Analysis, understood in a broad sense, and are a source of inspiration for new research. Most of the papers deal with various aspects of the theory, including classical topics in the geometry of convex bodies, inequalities involving volumes of such bodies or more generally, logarithmically-concave measures, valuation theory, probabilistic and isoperimetric problems in the combinatorial setting, volume distribution on high-dimensional spaces and characterization of classical constructions in Geometry and Analysis (like the Legendre and Fourier transforms, derivation and others). All the papers here are original research papers.
The -Cosine Transform and Intertwining Integrals on Real Grassmannians -- On Modules Over Valuations -- On Multiplicative Maps of Continuous and Smooth Functions -- Order Isomorphisms on Convex Functions in Windows -- Finite Transitive Graph Embeddings into a Hyperbolic -- Metric Space Must Stretch or Squeeze -- Tightness of Fluctuations of First Passage Percolation on Some Large Graphs -- Finitely Supported Measures on SL2(R) which are Absolutely Continuous at Infinity -- Interpolations, Convexity and Geometric Inequalities -- Hypercontractive Measures, Talagrand's Inequality, and Inuences -- A Family of Unitary Operators Satisfying a Poisson-Type Summation Formula -- Stability of Order Preserving Transforms -- On the Distribution of the 2-Norm of Linear Functionals on Isotropic Convex Bodies -- A Remark on Vertex Index of the Convex Bodies -- Inner Regularization of Log-Concave Measures and Small-Ball Estimates -- An Operator Equation Generalizing the Leibniz Rule for the Second Derivative -- Moments of Unconditional Logarithmically Concave Vectors -- Projections of Probability Distributions: A Measure-Theoretic Dvoretzky Theorem -- On a Loomis-Whitney Type Inequality for Permutationally Invariant Unconditional Convex Bodies -- The Hörmander Proof of the Bourgain-Milman Theorem -- On Some Extension of Feige's Inequality -- On the Mean Width of Log-Concave -- Approximate Gaussian Isoperimetry for k Sets -- Remark on Stability of Brunn-Minkowski and Isoperimetric Inequalities for Convex Bodies -- On Contact Points of Convex Bodies.
Keywords: Mathematics; Functional analysis; Discrete groups; Distribution (Probability theory).; Mathematics; Functional Analysis; Convex and Discrete Geometry; Probability Theory and Stochastic Processes