Suprematism in Harmonic Analysis

Preface.- Notions and terminology.- 1. Seven mathematical haikus.- 2. All those rectangles.- 3. As a needle turn: Besicovitch or Kakeya sets.- 4. Translation invariant operators.- 5. The multiplier problem for the ball.- 6. The ball multiplier on mixed norm spaces.- 7. The Poisson summation formula.- 8. Encounters at the interface with number theory.- 9. Weyl sums and atomic energy oscillations.- Bibliography.

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• Análise complexa, variáveis ??complexas
• Análise real, variáveis ??reais
• Análise funcional e transforma

Harmonic analysis;Hilbert transforms;Euclidean space;Basicovitch sets;Kakeya maximal function theorem;Poisson summation formula;Fourier analysis