場所: 立命館大学 BKC フォレストハウス1階 F107
時間:16:30 — 18:00
講演者:Freddy Delbaen(ETH and UNIZH)
André Martinez(University of Bologna and Ritsumeikan University)
講演者: Freddy Delbaen(ETH and UNIZH)
講演題目: Risk Measures, Orlicz Spaces and Mackey Topology
2. 17:20-18:00
講演者: André Martinez(University of Bologna and Ritsumeikan University)
講演題目: Optimal estimates for Helmholtz resonators with straight neck in any dimension.
アブストラクト: This is a joint work with Alain Grigis and Thomas Duykaerts where we obtain an optimal bound on the width of the lowest resonance for a general Helmholtz resonators with straight neck. Such a resonator consists of a bounded cavity, connected with the exterior by a thin tube. The frequency of the sounds it produces are determined by the shape of the cavity, and one expects that their duration is related to the length of the tube and to the diameter of its section. From a mathematical point of view, this phenomena is described by the resonances of the Dirichlet Laplacian on the domain consisting of the union of the cavity, the tube, and the exterior. Here, we obtain an asymptotic estimate on the duration of the sounds when the width of the tube tends to zero. This estimate shows that this duration is exponentially large, with a rate that is proportional to the length of the tube, and inversely proportional to its width. The proof is based on previous results obtained by Hislop-Martinez and Martinez-Nédélec, and on a recent version of Carleman estimates due to Kenig-Sjostrand-Uhlman.