Problems around Corona

In this paper the ill-posedness of Shannons sampling theorem is discussed and a regularized sampling algorithm for band-limited signals is presented. The convergence of the regularized sampling algorithm is studied and compared with Shannons sampling theorem by some examples. Diestel, Geoff, University of South Carolina Title: Maximal Bilinear Singular Integral Operators Associated with Planar Sets Abstract: Bounds for dyadic maximal operators are obtained for dilations of polygons and certain planar sets with smooth boundaries. In the case of polygons, the dyadic nature allows for some stronger results as well. Gatto, A. Eduardo, Institution: DePaul University Title: Lipschitz Spaces and Singular Integrals Associated to Non-doubling Measures Abstract: In 1916 Privalov proved that the Conjugate Function is a bounded operators on Lipschitz Spaces.In this talk we extend this result to Singular Integral Operators on a metric space with a nondoubling measure. Goldberg, Michael, Johns Hopkins University Title: The Schrödinger Equation with a Large Magnetic Potential Abstract: Many estimates for solutions of the Schrödinger equation remain valid even in the presence of a large fixed magnetic field, provided the field strength decays fast enough away from the origin. Kovalev, Leonid, Texas A&M University, Department of Mathematics Title: Quasiregular gradient mappings Abstract: Complex gradients of solutions of certain elliptic PDE are quasiregular mappings. However, not every quasiregular mapping is a gradient, and I am interested in the properties specific to gradients. Partly based on joint work with Al Baernstein II. Oh, Choonghong (Hiro), Dept of Math & Stats, UMASS, Amherst Title: On the local well-posedness of a one parameter family of coupled KdV systems Abstract: We consider a system of two coupled nonlinear equations of Korteweg-de Vries (KdV) type arising in oceanography and introduced by A. Majda and J. Biello. Of special interest in its applications is the periodic set-