and Applied Analysis 3 In two main theorems in 20 , the authors proved the following results, which we now incorporate in the next theorem. Theorem A. Assume p ≥ 1 and φ is a holomorphic self-map of Π . Then the following statements true hold. a The operator Cφ : H Π → A∞ Π is bounded if and only if sup z∈Π Im z ( Imφ z )1/p < ∞. 1.8 b The operator Cφ : H Π → B∞ Π is bounded if and only if sup ...

First, we introduce some basic notation which is used in this paper. Throughout the entire paper, the unit disk in the finite complex plane C will be denoted by D. H D will denote the space of all analytic functions on D. Every analytic self-map φ of the unit disk D induces through composition a linear composition operator Cφ fromH D to itself. It is a well-known consequence of Littlewood’s sub...

Let φ(z) = (φ1(z), · · · , φn(z)) be a holomorphic self-map of B and ψ(z) a holomorphic function on B, where B is the unit ball of C n . Let 0 < p, s < +∞,−n−1 < q < +∞, q + s > −1 and α ≥ 0, this paper gives some necessary and sufficient conditions for the weighted composition operator Wψ,φ induced by φ and ψ to be bounded and compact between the space F (p, q, s) and α-Bloch space β.

In this paper, we firstly consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalized Uhlmann theorem in an infinite dimension Hilbert space. Also, we show that S(Φ(ρ)) = S(ρ) for all quantum states ρ if and only if there exists an isometry operator V such that Φ(ρ) = V ρV , where Φ is a quantum cha...

For j = 1, ..., n, letΩj be open sets of the complex plane and let φj be holomorphic functions on Ωj such that φ′′ j does not vanish identically on Ωj . We consider φ (z1, ..., zn) = φ1 (z1) + ...+ φn (zn). We characterize the pairs (p, q) such that the convolution operator with the surface measure supported on a compact subset of the graph of φ is p− q bounded.

We show that the actuality operator A is redundant in any propositional modal logic characterized by a class of Kripke models (respectively, neighborhood models). Specifically, we prove that for every formula φ in the propositional modal language with A, there is a formula ψ not containing A such that φ and ψ are materially equivalent at the actual world in every Kripke model (respectively, nei...

which governs a classical motion in the space of link variables. φ is the pseudofermion field, whereas P is the canonical momenta, which is randomized at the beginning of each trajectory. For the classical motion we need the gauge derivative of pseudofermionic action, namely the fermion force. For the fermion force one needs to invert the overlap operator on the φ field: force = −ψ dDD dU ψ, wh...

We define new classes of the family E(Φ,Ψ), in a unit disk U := {z ∈ C, |z| < 1}, as follows: for analytic functions F (z),Φ(z) and Ψ(z) so that <{ (z)∗Φ(z) F (z)∗Ψ(z)} > 0, z ∈ U, F (z) ∗Ψ(z) 6= 0 where the operator ∗ denotes the convolution or Hadamard product. Moreover, we establish some subordination results for these new classes.