Harmonic Analysis in Italy



General scientific framework.

Classically harmonic analysis is concerned with the properties of Fourier transforms and Fourier series, in particular convergence of summability methods, the treatment of convolution operators and the applications to complex analysis, partial differential equations and approximation theory. Modern harmonic analysis has also enlarged its views to encompass analytical problems posed on a Lie group or a homogeneous space instead of Rn. Symmetric spaces provide the most natural context in this regard. Discrete structures, such as buildings and graphs, are another context in which to study these problems. They often provide a simpler analytical model to test conjectures and techniques that can be used to solve analogous problems on symmetric spaces. On the more applied side, one of the most successful outputs of Fourier analysis of the last ten years is the theory of wavelets, which has become an important branch of numerical and applied mathematics. Besides these applied aspects, wavelets present many interesting theoretical aspects related to approximation theory, to harmonic analysis in phase space and to square integrable representations of Lie groups. The Italian research network in Harmonic Analysis is concerned with all these aspects of the subject.

Research project.

The research project is divided in five topics. See the local units for more details.
  1. Fourier analysis (Milano, Pisa, Torino)

  2. Harmonic analysis on Lie groups and homogeneous spaces (Genova, Milano, Pisa, Roma, Sassari, Torino)

  3. Wavelets (Genova, Milano, Torino)

  4. Harmonic analysis on discrete structures (Genova, Milano, Roma, Sassari)

  5. Methods of harmonic analysis for differential and integral operators (Genova, Milano, Pisa, Roma, Sassari, Torino)

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Harmonic Analysis in Italy -->[ Local units: Genova  -  Milano  -  Pisa  -  Roma  -  Sassari  -  Torino ]