Landscapes of Time-Frequency Analysis

1. Front Matter

   Pages i-xviii

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2. On the Probabilistic Cauchy Theory for Nonlinear Dispersive PDEs

   • Árpád Bényi, Tadahiro Oh, Oana Pocovnicu

   Pages 1-32

3. Endpoint Results for Fourier Integral Operators on Noncompact Symmetric Spaces

   • Tommaso Bruno, Anita Tabacco, Maria Vallarino

   Pages 33-58

4. Weak-Type Estimates for the Metaplectic Representation Restricted to the Shearing and Dilation Subgroup of \(SL(2,\mathbb {R})\)

   • Francesca M. Gasparini

   Pages 59-73

5. On the Atomic Decomposition of Coorbit Spaces with Non-integrable Kernel

   • Stephan Dahlke, Filippo De Mari, Ernesto De Vito, Lukas Sawatzki, Gabriele Steidl, Gerd Teschke et al.

   Pages 75-144

6. On the Purity and Entropy of Mixed Gaussian States

   • Maurice de Gosson

   Pages 145-158

7. On the Continuity of \(\tau \)-Wigner Pseudodifferential Operators

   • Lorenza D’Elia

   Pages 159-171

8. Gabor Expansions of Signals: Computational Aspects and Open Questions

   • Hans G. Feichtinger

   Pages 173-206

9. \(L^p\) Continuity and Microlocal Properties for Pseudodifferential Operators

   • Gianluca Garello, Alessandro Morando

   Pages 207-224

10. Hyperbolic Wavelet Frames and Multiresolution in the Weighted Bergman Spaces

    • Margit Pap

    Pages 225-247

11. Infinite Order Pseudo-Differential Operators

    • Stevan Pilipović, Bojan Prangoski

    Pages 249-276

12. New Progress on Weighted Trudinger–Moser and Gagliardo–Nirenberg, and Critical Hardy Inequalities on Stratified Groups

    • Michael Ruzhansky, Nurgissa Yessirkegenov

    Pages 277-289

13. Continuity Properties of Multilinear Localization Operators on Modulation Spaces

    • Nenad Teofanov

    Pages 291-307

14. Semi-continuous Convolution Estimates on Weakly Periodic Lebesgue Spaces

    • Joachim Toft

    Pages 309-321

15. Almost Diagonalization of Pseudodifferential Operators

    • S. Ivan Trapasso

    Pages 323-342

16. Correction to: Weak-Type Estimates for the Metaplectic Representation Restricted to the Shearing and Dilation Subgroup of \(SL(2,\mathbb {R})\)

    • Francesca M. Gasparini

    Pages C1-C1

17. Back Matter

    Pages 343-347

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The chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications.  New connections between different but related areas were presented in the context of time-frequency analysis, encouraging future research and collaborations.  Some of the topics covered include:

• Abstract harmonic analysis,
  
• Numerical harmonic analysis,
  
• Sampling theory,
  
• Compressed sensing,
  
• Mathematical signal processing,
  
• Pseudodifferential operators, and
  
• Applications of harmonic analysis to quantum mechanics.

Landscapes of Time-Frequency Analysis will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.

• Harmonic analysis
• Fourier analysis
• Time-frequency analysis
• Pseudodifferential operators
• Sampling theory
• Compressed sensing
• Mathematical signal processing
• Applications of harmonic analysis to quantum mechanics
• Gabor frames
• Modulation spaces
• Fourier integral operators
• partial differential equations

• Dipartimento di Matematica “G. Peano”, University of Torino, Turin, Italy

  Paolo Boggiatto, Elena Cordero, Alessandro Oliaro

• Faculty of Mathematics, University of Vienna, Vienna, Austria

  Maurice de Gosson, Hans G. Feichtinger

• Department of Mathematical Sciences, Polytechnic University of Torino, Turin, Italy

  Fabio Nicola, Anita Tabacco

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