We represent a classical Maxwell-Bloch equation and related to it positive part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is given by an infinitesimal action of a nilpotent subalgebra n+ of affine Lie algebra ŝl2 on a Maxwell-Bloch phase space treated as a homogeneous space of n+. A space of local integrals of motion is described using cohomology methods. We show t...

In this paper, we characterize those holomorphic symbols u on the unit ball B and holomorphic self-mappings φ of B for which the weighted composition operator uCφ is bounded or compact from Bloch-type space to H∞ space. Mathematics subject classification (2010): Primary 47B33; Secondary 47B38.

The boundedness of the weighted differentiation composition operator from the logarithmic Bloch space to the weighted-type space is characterized in terms of the sequence (zn)n∈N0 . An asymptotic estimate of the essential norm of the operator is also given in terms of the sequence, which gives a characterization for the compactness of the operator.

Products of integral-type and composition operators has been recently introduced by Li and Stević and studied in a series of their papers. In this note we study the boundedness and compactness of these products from generally weighted Bloch space to F (p, q, s) space, where 0 < p, s < ∞, q > −2, α > 0.

We present some characterizations for the compactness of difference two composition operators acting between analytic Besov spaces and weighted little Bloch type space over unit disk.