Schrödinger Equation and Oscillatory Hilbert Transforms of Second Degree.
The main purpose of this article is to give a new method and new results on a very old topic: the comparison of the Riemann processes of summation (R,κ) with other summation processes. The motivation comes from the study of continuous unimodular functions on the circle, their Fourier series and their winding numbers. My oral presentation in Poznań at the JM-100 conference exposed the ways by which this study was developed since the fundamental work of Brézis and Nirenberg on the topological degree...
Les applications continues du cercle dans ont des séries de Fourier intéressantes : le théorème établi ici dit que si les coefficients de Fourier sont de carré sommable avec certains poids pour , il en est de même pour . C’est encore vrai pour , mais faux pour les applications mesurables bornées.