The interaction between a Bloch and a Néel wall in the parametrically driven nonlinear Schrödinger equation is studied by following the dissociation of their unstable bound state. Mathematically, the analysis focuses on the splitting of a fourfold zero eigenvalue associated with a pair of infinitely separated Bloch and Néel walls. It is shown that a Bloch and a Néel wall interact as two classic...

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...

Norm and essential norm of differences of differentiation composition operators between Bloch spaces have been estimated in this paper. As a result, we find characterizations for boundedness and compactness of these operators.

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.

In this paper we give a new description, in terms of optomechanics, of previous work on the problem of an atomic Bose–Einstein condensate interacting with the optical lattice inside a laser-pumped optical cavity and subject to a bias force, such as gravity. An atomic wave packet in a tilted lattice undergoes Bloch oscillations; in a high-finesse optical cavity the backaction of the atoms on the...

We report on the observation of Bloch oscillations in light transport through periodic dielectric systems. By introducing a linear refractive index gradient along the propagation direction the optical equivalent of a Wannier-Stark ladder was obtained. Bloch oscillations were observed as time-resolved oscillations in transmission, in direct analogy to electronic Bloch oscillations in conducting ...

A description of the closure in the Bloch norm of the Bloch functions that are in a Hardy space is given. The result uses the classical estimates for the Lusin area function. §