We study subharmonic functions in the unit ball of R , with either a Bloch–type growth or a growth described through integral conditions involving some involutions of the ball. Considering mappings u 7→ gu between sets of functions with a prescribed growth, we study how the choice of these sets is related to the growth of the function g.

We study the boundedness and compactness of the differences of two weighted composition operators acting from the Bloch space B to the space H∞ of bounded analytic functions on the open unit disk. Such a study has a relationship to the topological structure problem of composition operators on H∞. Using this relation, we will estimate the operator norms and the essential norms of the differences...

A function theoretic characterization is given of when a composition operator is compact on BMOA, the space of analytic functions on the unit disk having radial limits that are of bounded mean oscillation on the unit circle. When the symbol of the composition operator is univalent, compactness on BMOA is shown to be equivalent to compactness on the Bloch space, and a characterization in terms o...

Catanese surfaces are regular surfaces of general type with pg = 0. They specialize to double covers of Barlow surfaces. We prove that the CH0 group of a Catanese surface is equal to Z, which implies the same result for the Barlow surfaces.

We consider a particle of half-integer spin which is nonrelativistic in the rest frame. Assuming the particle is completely polarized along third axis we calculate the Bloch vector as seen by a moving observer. The result for its length is expressed in terms of dispersion of some vector operator linear in momentum. The relation with the localization properties is discussed. ∗supported by the Ló...

Introduction: Prostate cancer (PCa) is the most prevalent malignant tumor in the male population worldwide and it is the second leading cause of cancer-related death in males. PCa is almost incurable due to the resistance of PCa to conventional treatments. Cancer stem cells (CSCs) theory suggests that a small subpopulation of cancer cells is responsible for tumor development, ...