in this paper boundedness and compactness of generalized composition oper-ators from logarithmic bloch type spaces to q_k type spaces are investigated.

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.

We prove that the Bloch space coincides with the space BMOA in the tube over the spherical cone of R.3; this extends a well-known onedimensional result. Introduction. Let Q be a symmetric Siegel domain of type II contained in Cn. Let V denote the Lebesgue measure in fi and H{Q) the space of holomorphic (or analytic) functions in fi. When n = 1 and fi = tt+ = {z £ C: Imz > 0}, a Bloch function i...

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...

A Bloch ion has periodic symmetry and is distributed in space in a lattice array form. Its spatial density distribution is neutralized within each unit cell by a metal's electrons. The wave function repeats coherently modulo a Bravais lattice vector. Paired Bloch deuterons partitioned over a sufficiently large number of unit cells become superposed and coherently mixed by coordinate exchange. A...

Let X be a complex Banach space and let Bloch(X) denote the space of X-valued analytic functions on the unit disc verifying that sup|z|<1(1−|z|)||f ′(z)|| < ∞. A sequence (Tn)n of bounded operators between two Banach spaces X and Y is said to be an operator-valued multiplier between Bloch(X) and 1(Y ) if the map ∑∞ n=0 xnz n → (Tn(xn))n defines a bounded linear operator from Bloch(X) into 1(Y )...

Given an orientable complete hyperbolic 3-manifold of finite volume M we construct a canonical class α(M) in H3(B(SL2(C), T)) with B(SL2(C), T) the SL2(C)-orbit space of the classifying space for a certain family of isotropy subgroups. We prove that α(M) coincides with the Bloch invariant β(M) of M defined by Neumann and Yang in [13], giving with this a simpler proof that the Bloch invariant is...

ND band state D+ ions are treated as a sum over pairs. The wave functions of a D+ pair is assumed to be a product of a Bloch function in lattice space times a Bloch function in separation space. Overlap allows a strong force fusion reaction to 4He++. A coupling between the nuclear change and the ion charge distribution in the lattice is described. The change in ion charge distribution scatters ...