Preface of the Proceedings of the "Analysis, Operator Theory, and Mathematical Physics" Workshop (February 24-28, 2014, Ixtapa, Guerrero, México)

Abstract

This issue of Communications in Mathematical Analysis is devoted to various aspects of Analysis, Operator Theory and their applications in problems of Mathematical Physics. In particular, in this volume there are studied the compactness of commutators of convolution type operators with piecewise quasicontinuous data on weighted Lebesgue spaces with Muchkenhoupt weights, regularizers of Mellin pseudodifferential operators with slowly oscillating symbols of limited smoothness, the diffraction by a half-plane with different face impedances on an obstacle perpendicular to the boundary by using the theory of Wiener-Hopf and Hankel type operators on Bessel potential spaces. It is shown that the discrete series of irreducible unitary representation spaces of the non-compact group SO(2,1) can be naturally interpreted as discrete versions of the linear harmonic oscillator in standard non-relativistic quantum mechanics. Several papers in this volume are devoted to the structural analysis of Toeplitz operators with various specific classes of generating symbols and of the algebras generated by such Toeplitz operators. In particular, Toeplitz operators with quasi-radial symbols acting on the weighted Bergman space on the unit ball, Toeplitz operators with quasi-radial quasi-homogeneous symbols acting on the weighted pluriharmonic Bergman spaces on the unit ball, and Toeplitz operators with angular symbols acting on the Bergman spaces on the upper half-plane are studied. The Fredholm symbol algebras for the C-algebra generated by Toeplitz operators with piecewise quasicontinuous symbols and for the C-algebra generated by Toeplitz operators with piecewise continuous and slowly oscillating symbols, both acting on the Bergman space on the unit disk, are described.