On a problem of Kahane in higher dimensions

On a problem of Kahane in higher dimensions

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Jim Wright , University of Edinburgh
Fine Hall 322

Please note special day, time and room.   We characterise those real analytic mappings from T^k to T^d which map absolutely convergent Fourier series on T^d to uniformly convergent Fourier series via composition. We do this with respect to rectangular summation on T^k. We also investigate uniform convergence with respect to square sums and highlight the differences which arise.