Harmonic Analysis and PDE 2019 Conference Program: Tuesday, May 28

09:30-10:15

Alexander L. Skubachevskii

Peoples' Friendship University of Russia ,Russia

The Kato conjecture for some classes of nonlocal operators
 

Abstract: The Kato conjecture for some classes of nonlocal operators In 1961, T. Kato has formulated the following problem: “Is it true that the domain of square root from regular accretive operator is equal to the domain of square root from adjoint operator?”

Sufficient conditions for fulfilment of the Kato conjecture were studied by T. Kato, J. Lions and others. J. Lions has proved that strongly elliptic differential operators of 2m order with smooth coefficients and homogeneous Dirichlet conditions on a smooth boundary satisfy the Kato conjecture. For strongly elliptic differential operators of 2m order with measurable bounded coefficients corresponding result was obtained by P. Auscher, S. Hofman, A. McIntosh, and P. Tchamitchian.

In this lecture we consider two types of nonlocal elliptic operators: strongly elliptic functional differential operators and elliptic differential-difference operators with degeneration. We prove that these operators satisfy the Kato square root conjecture, see [1, 2]. The publication has been prepared with the support of the “RUDN University Program 5-100” and the Russian Foundation for Basic Research (project No. 17-01-00401).

Armen Sergeev

Steklov Mathematical Institute, Russia

Adiabatic Limit in Ginzburg-Landau and Seiberg-Witten Equations

Pekka Koskela

University of Jyväskylä, Finland

Functional properties of Sobolev extensions
 

Abstract: Functional properties of Sobolev extensions A given domain Ω in a Euclidean space may or may not have the property that each function in a Sobolev space over this domain can be extended to a function in the analogous Sobolev space over the entire Euclidean space.

I will review functional properties of this condition, e.g. invariance under a change of variable. Some of the results are from a manuscript that is about to be finished.

Yehuda Pinchover

Technion - Israel Institute of technology, Israel

On the equivalence of heat kernels of second-order parabolic operators

14:15-14:45

Leonid Zelenko

University of Haifa, Israel

Conditions of discreteness of the spectrum for the multi - dimensional Schrödinger operator and some optimization problems for capacity and   measures

14:50-15:20

Mikhail L. Goldman

Peoples' Friendship University of Russia,   Russia
Optimal envelope for the cone of moduli of continuity for Generalized Bessel potentials

Elza G. Bakhtigareeva,

Peoples' Friendship University of  Russia, Russia
Sharp estimates for the Hardy operator in a weighted Orlicz space 

Alexander Isaev

The Australian National University, Australia

Zero CR-curvature equations for Levi-degenerate manifolds

Boris Solomyak

Bar-Ilan University, Israel

Survey of self-similar measures

Vladimir P. Golubyatnikov

Novosibirsk State University, Russia
Non-uniqueness of cycles in block-linear dynamics

Evgeny Derevtsov

Sobolev Institute of Mathematics SB RAS, Russia
Differential equations and integral operators at investigations   of integral geometry and tomography problems

Mark G. Lawrence

Nazarbayev University, Kazakhstan

Bergman spaces of real analytic functions

Victor Gichev

Sobolev Institute of Mathematics, Omsk Branch, Russia

On complex spherical harmonics on S²

Vladimir Gol'dshtein

Ben-Gurion University of the Negev, Israel

Composition operators on Sobolev spaces and Divergent Elliptic Operators

Alexander Ukhlov

Ben-Gurion University of the Negev, Israel

Composition operators on Sobolev spaces and spectral Estimates   of non-linear elliptic operators

Pavel Shvartsman

Technion - Israel Institute of Technology, Israel

On the boundary values of C²-functions

Conference dinner in the restaurant "Nostalgia"

Rishon LeZion