Morphisms of Klein surfaces.
We give an elementary proof of a theorem of Andreian Cazacu on the behavior of morphisms of Klein surfaces under composition.
We give an elementary proof of a theorem of Andreian Cazacu on the behavior of morphisms of Klein surfaces under composition.
A compact Riemann surface X of genus g≥2 which admits a cyclic group of automorphisms C q of prime order q such that X/C q has genus 0 is called a cyclic q-gonal surface. If a q-gonal surface X is also p-gonal for some prime p≠q, then X is called a multiple prime surface. In this paper, we classify all multiple prime surfaces. A consequence of this classification is a proof of the fact that a cyclic q-gonal surface can be cyclic p-gonal for at most one other prime p.
We show that T is a surjective multiplicative (but not necessarily linear) isometry from the Smirnov class on the open unit disk, the ball, or the polydisk onto itself, if and only if there exists a holomorphic automorphism Φ such that T(f)=f ○ Φ for every class element f or T(f) = for every class element f, where the automorphism Φ is a unitary transformation in the case of the ball and Φ(z 1, ..., z n) = for |λ j| = 1, 1 ≤ j ≤ n, and (i 1; ..., i n)is some permutation of the integers from...
We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.
We study estimates for the solution of the equation du=f in one variable. The new ingredient is the use of holomorphic functions with precise growth restrictions in the construction of explicit solution to the equation.
In 1966 de Branges and Rovnyak introduced a concept of complementation associated to a contraction between Hilbert spaces that generalizes the classical concept of orthogonal complement. When applied to Toeplitz operators on the Hardy space of the disc, H2, this notion turned out to be the starting point of a beautiful subject, with many applications to function theory. The work has been in constant progress for the last few years. We study here the multipliers of some de Branges-Rovnyak spaces...