第６回調和解析中央大セミナー

時間：14:00～15:00
講演者：Luigi Forcella 氏（Scuola Normale Superiore, Pisa）

題目：Double scattering channels for 1D NLS and a generalization to higher dimensions

概要：We consider a class of 1D NLS perturbed with a steplike potential. We prove that
the nonlinear solutions satisfy the double scattering channels in the energy space. The
proof is based on concentration-compactness/rigidity method. We prove moreover that
in dimension higher than one, classical scattering holds if the potential is periodic in all
but one dimension and is steplike and repulsive in the remaining one.

時間：15:30～17:00
講演者：Jasson Vindas 氏 (Ghent University, Belgium)

題目：Asymptotic distribution of Beurling's generalized prime numbers

概要：This talk is a survey on classical and recent results concerning the asymptotic
distribution of generalized prime numbers.
The goal of Beurling's generalized prime number theory is to replace the ordinary
prime numbers by a rather arbitrary non-decreasing sequence of positive real numbers (generalized primes), consider then the multiplicative semigroup generated by it (generalized integers), and then establish relations between asymptotic properties of the counting functions of the generalized primes and integers.
We will discuss various conditions that ensure the validity of the prime number theorem in this context.