Harmonic Analysis and PDE 2019 Conference Program: Thursday, May 30

09:30-10:15

Victor Burenkov
Peoples' Friendship University of Russia, Russia

Interpolation theory and local Morrey-type spaces

Matania Ben-Artzi

Hebrew University of Jerusalem, Israel

From crystals to Dirac operators-spectral theory

Abstract: We consider constant coefficient first–order partial differential systems, homogeneous and non–homogeneous, and their potential perturbations. It is assumed that the homogeneous part is strongly propagative. In the nonhomegeneous case it is assumed that the operator is isotropic . The spectral theory of such systems and their potential perturbations is expounded, and a Limiting Absorption Principle is obtained up to thresholds. Special attention is given to a detailed study of the Dirac (massive and massless) and Maxwell operators. The estimates of the spectral derivative near the thresholds are based on trace estimates on the slowness surfaces. Two applications of these estimates are presented: 1) Global spacetime estimates of the associated evolution unitary groups, that are also commonly viewed as decay estimates. While analogous estimates exist for the Dirac operator, our decay estimates for the Maxwell system are completely new. 2) The finiteness of the eigenvalues (in the spectral gap) of the perturbed Dirac operator is studied, under suitable decay assumptions on the potential perturbation. This is a joint work with T. Umeda.

11:35-12:10

Alex Iosevich

University of Rochester, USA

The role of curvature in frame theory

Abstract: We are going to discuss the question of the existence of Fourier bases and frames in a variety of Hilbert spaces. We are going to exhibit a class of measures where the corresponding Hilbert space does not possess a frame of exponentials. We are going to discuss the connection between this problem and a variety of questions in geometric measure there.

12:15-12:45

Jacob (Koby) Rubinstein

Technion - Israel Institute of Technology, Israel
 

Optimal transport and geometric optics

The classical Fermat principle of least time forms the foundation of geometric optics. We introduce a new principle, that we call the Weighted Least Action Principle, that generalizes the Fermat principle, and moreover deals with measurable quantities. We then show that the new principle is equivalent to the Monge optimal transport problem for a specific cost function. Moreover, we argue that all critical points of the Monge functional are optically relevant. The theoretical analysis is accompanied with experimental results that demonstrate its applicability. Joint work with Gershon Wolansky.

14:00-14:30

Lucian Beznea

Simion Stoilow Institute of Mathematics of the Romanian Academy and University of Bucharest, Romania

Connections between the Dirichlet and the Neumann problem for integrable boundary data

Lavi Karp

ORT Braude College, Israel

The continuity of the flow map for quasilinear symmetric Hyperbolic systems

Ron Peled

Tel Aviv University, Israel

Existence of combinatorial structures via asymptotics of integrals

16:05-16:35

Darya Apushkinskaya

Peoples' Friendship University of Russia, Russia and Saarland University, Germany                    

Free boundaries in problems with hysteresis 

Samuel L. Krushkal

Bar-Ilan University, Israel

A general coefficient theorem for univalent functions

Gershon Kresin

Ariel University, Israel
Sharp pointwise estimates for solutions to some equations of mathematical physics

Akram Begmatov

Samarkand State University, Uzbekistan
Integral geometry and integral equations of the first kind: Theory and Applications