On the computation of bounds for low energy Compton scattering parameters : proof of a conjecture
Let be a rectifiable Jordan curve in the finite complex plane which is regular in the sense of Ahlfors and David. Denote by the space of all complex-valued functions on which are square integrable w.r. to the arc-length on . Let stand for the space of all real-valued functions in and put Since the Cauchy singular operator is bounded on , the Neumann-Poincaré operator sending each into is bounded on . We show that the inclusion characterizes the circle in the class of all...
We give several characterizations of the symmetrized n-disc Gₙ which generalize to the case n ≥ 3 the characterizations of the symmetrized bidisc that were used in order to solve the two-point spectral Nevanlinna-Pick problem in ℳ ₂(ℂ). Using these characterizations of the symmetrized n-disc, which give necessary and sufficient conditions for an element to belong to Gₙ, we obtain necessary conditions of interpolation for the general spectral Nevanlinna-Pick problem. They also allow us to give a...
We consider the space of holomorphic functions at the origin which extend analytically on the universal covering of , . We show that this space is stable by convolution product, thus is a resurgent algebra.