On the setting of Siegel upper half-space we study spaces bounded and vanishing mean oscillations which are defined in terms Berezin transform, use them to characterize compact Hankel operators on Bergman space. When symbols specialized be holomorphic, its corresponding Bloch space half-space.

It is well-known that the chiral WZNW Bloch waves satisfy a quadratic classical exchange algebra which implies the affine Kac-Moody algebra for the corresponding currents. We here obtain a direct derivation of the exchange algebra by inverting the symplectic form on the space of Bloch waves, and give a completely algorithmic construction of its generalized free field realizations that extend th...

Let φ and ψ be analytic self-maps of the open unit disk D . Using pseudo-hyperbolic distance ρ(φ ,ψ) , we characterize the boundedness and compactness of the differences of generalized composition operators (C φ −Ch ψ ) f (z) = ∫ z 0 [ f ′(φ(ξ ))g(ξ )− f ′(ψ(ξ ))h(ξ )]dξ , z ∈ D between two Bloch-type spaces on D . The results generalize the corresponding results on the single generalized compo...

A microscopic theory for the interaction between semiconductor quantum well structures and laser eld based on the semiconductor Bloch equations is applied to vertical-cavity surface-emitting lasers (VCSELs) with the inclusion of plasma heating. The semiconductor Bloch equations are reduced to those for the rst and second moments of the carrier density distributions in the carrier wave vector. P...

The space of Bloch functions on bounded symmetric domains is extended by considering f f the unit ball alttext="upper B Subscript upper E"> <...

The spinor representation of spin-1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Bloch-sphere rotations to be represented as quaternionic multiplications, simplifying the form of the dynamical equations. Left-multiplications generally correspond to non-unita...