10/01/2014, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Yuri Karlovich, Universidad Autónoma del Estado de Morelos, Cuernavaca, México
\(C^\ast\)-algebras of two-dimensional singular integral operators
with solvable groups of shifts
Fredholm symbol calculi for the \(C^\ast\)-algebras generated by
the \(C^\ast\)-algebra of two-dimensional singular integral
operators with continuous coefficients on a bounded closed simply
connected plane domain with Liapunov boundary and by unitary shift
operators associated with discrete solvable groups being semidirect
products of commutative groups of conformal mappings (elliptic,
hyperbolic or parabolic) and cyclic groups generated by reflections
are constructed. As a result, we establish Fredholm criteria for
the operators in considered algebras. The talk is based on a joint
work with V. Mozel.