Geometric Aspects of Functional Analysis

1. Front Matter

   Pages i-viii

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2. The α-Cosine Transform and Intertwining Integrals on Real Grassmannians

   • Semyon Alesker

   Pages 1-21

3. On Modules Over Valuations

   • Semyon Alesker

   Pages 23-34

4. On Multiplicative Maps of Continuous and Smooth Functions

   • Shiri Artstein-Avidan, Dmitry Faifman, Vitali Milman

   Pages 35-59

5. Order Isomorphisms on Convex Functions in Windows

   • Shiri Artstein-Avidan, Dan Florentin, Vitali Milman

   Pages 61-122

6. Finite Transitive Graph Embeddings into a Hyperbolic Metric Space Must Stretch or Squeeze

   • Itai Benjamini, Oded Schramm

   Pages 123-126

7. Tightness of Fluctuations of First Passage Percolation on Some Large Graphs

   • Itai Benjamini, Ofer Zeitouni

   Pages 127-132

8. Finitely Supported Measures on \(S{L}_{2}(\mathbb{R})\) Which are Absolutely Continuous at Infinity

   • Jean Bourgain

   Pages 133-141

9. Moebius Schrödinger

   • Jean Bourgain

   Pages 143-150

10. Interpolations, Convexity and Geometric Inequalities

    • Dario Cordero-Erausquin, Bo’az Klartag

    Pages 151-168

11. Hypercontractive Measures, Talagrand’s Inequality, and Influences

    • Dario Cordero-Erausquin, Michel Ledoux

    Pages 169-189

12. A Family of Unitary Operators Satisfying a Poisson-Type Summation Formula

    • Dmitry Faifman

    Pages 191-204

13. Stability of Order Preserving Transforms

    • Dan Florentin, Alexander Segal

    Pages 205-225

14. On the Distribution of the ψ2-Norm of Linear Functionals on Isotropic Convex Bodies

    • Apostolos Giannopoulos, Grigoris Paouris, Petros Valettas

    Pages 227-253

15. A Remark on Vertex Index of the Convex Bodies

    • Efim D. Gluskin, Alexander E. Litvak

    Pages 255-265

16. Inner Regularization of Log-Concave Measures and Small-Ball Estimates

    • Bo’az Klartag, Emanuel Milman

    Pages 267-278

17. An Operator Equation Generalizing the Leibniz Rule for the Second Derivative

    • Hermann König, Vitali Milman

    Pages 279-299

18. Moments of Unconditional Logarithmically Concave Vectors

    • Rafał Latała

    Pages 301-315

19. Projections of Probability Distributions: A Measure-Theoretic Dvoretzky Theorem

    • Elizabeth Meckes

    Pages 317-326

20. On a Loomis–Whitney Type Inequality for Permutationally Invariant Unconditional Convex Bodies

    • Piotr Nayar, Tomasz Tkocz

    Pages 327-333

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.

• 80M35, 26A51, 32-XX, 46-XX, 60-XX
• Asymptotic Geometric Analysis
• Functional Analysis
• Geometric Inequalities
• Probability Theory

• Tel-Aviv, Israel

  Bo'az Klartag

• Technion Machine Learning Center, Technion, Israel Institute of Technology, Technion City, Haifa, Israel

  Shahar Mendelson

• Fac. Exact Sciences, School of Mathematical Sciences, University of Tel Aviv, Tel Aviv, Israel

  Vitali D. Milman

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