Trends in Harmonic Analysis

1. Front Matter

   Pages I-XII

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2. The Shifted Wave Equation on Damek–Ricci Spaces and on Homogeneous Trees

   • Jean-Philippe Anker, Pierre Martinot, Emmanuel Pedon, Alberto G. Setti

   Pages 1-25

3. Invariance of Capacity Under Quasisymmetric Maps of the Circle: An Easy Proof

   • Nicola Arcozzi, Richard Rochberg

   Pages 27-32

4. A Koksma–Hlawka Inequality for Simplices

   • Luca Brandolini, Leonardo Colzani, Giacomo Gigante, Giancarlo Travaglini

   Pages 33-46

5. A Dual Interpretation of the Gromov–Thurston Proof of Mostow Rigidity and Volume Rigidity for Representations of Hyperbolic Lattices

   • Michelle Bucher, Marc Burger, Alessandra Iozzi

   Pages 47-76

6. The Algebras Generated by the Laplace Operators in a Semi-homogeneous Tree

   • Enrico Casadio Tarabusi, Massimo A. Picardello

   Pages 77-90

7. Surjunctivity and Reversibility of Cellular Automata over Concrete Categories

   • Tullio Ceccherini-Silberstein, Michel Coornaert

   Pages 91-133

8. Pointwise Convergence of Bochner–Riesz Means in Sobolev Spaces

   • Leonardo Colzani, Sara Volpi

   Pages 135-146

9. Sub-Finsler Geometry and Finite Propagation Speed

   • Michael G. Cowling, Alessio Martini

   Pages 147-205

10. On the Boundary Behavior of Holomorphic and Harmonic Functions

    • Fausto Di Biase

    Pages 207-244

11. Constructing Laplacians on Limit Spaces of Self-similar Groups

    • Alfredo Donno

    Pages 245-275

12. Some Remarks on Generalized Gaussian Noise

    • Saverio Giulini

    Pages 277-290

13. Eigenvalues of the Vertex Set Hecke Algebra of an Affine Building

    • Anna Maria Mantero, Anna Zappa

    Pages 291-369

14. A Liouville Type Theorem for Carnot Groups: A Case Study

    • Alessandro Ottazzi, Ben Warhurst

    Pages 371-380

15. Stochastic Properties of Riemannian Manifolds and Applications to PDE’s

    • Gregorio Pacelli Bessa, Stefano Pigola, Alberto G. Setti

    Pages 381-398

16. Characterization of Carleson Measures for Besov Spaces on Homogeneous Trees

    • Maria Rosaria Tupputi

    Pages 399-407

17. Atomic and Maximal Hardy Spaces on a Lie Group of Exponential Growth

    • Maria Vallarino

    Pages 409-424

18. The Maximal Singular Integral: Estimates in Terms of the Singular Integral

    • Joan Verdera

    Pages 425-447

This book illustrates the wide range of research subjects developed by the Italian research group in harmonic analysis, originally started by Alessandro Figà-Talamanca, to whom it is dedicated in the occasion of his retirement. In particular, it outlines some of the impressive ramifications of the mathematical developments that began when Figà-Talamanca brought the study of harmonic analysis to Italy; the research group that he nurtured has now expanded to cover many areas. Therefore the book is addressed not only to experts in harmonic analysis, summability of Fourier series and singular integrals, but also in potential theory, symmetric spaces, analysis and partial differential equations on Riemannian manifolds, analysis on graphs, trees, buildings and discrete groups, Lie groups and Lie algebras, and even in far-reaching applications as for instance cellular automata and signal processing (low-discrepancy sampling, Gaussian noise).

• Analysis on discrete groups and graphs
• Harmonic Analysis
• Hecke algebras on Bruhat-Tits affine buildings
• Lie groups and symmetric spaces
• Potential Theory

• Dipto. Matematica, Università di Roma - Tor Vergata, Roma, Italy

  Massimo A. Picardello

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