Sunglasses Ray Ban AAA Black Rayban-3404,f∈Xf∈X satisfying fθ∈Yfθ∈Y must actually satisfy
If X⊂YX⊂Y are two classes of analytic functions in the unit disk DD and θ is an inner function, θ is said to be (X,Y)(X,Y)-improving , if every function f∈Xf∈X satisfying fθ∈Yfθ∈Y must actually satisfy fθ∈Xfθ∈X. This notion has been recently introduced by K.M. Dyakonov. In this paper we study Sunglasses Ray Ban AAA Black Rayban-3404 the (X,Y)(X,Y)-improving inner functions for several pairs of spaces (X,Y)(X,Y). In particular, we prove that for any p∈(0,1)p∈(0,1) the (Qp,BMOA)(Qp,BMOA)-improving inner functions and the (Qp,B)(Qp,B)-improving inner functions are precisely the inner functions which belong to the space QpQp. Here, BB is the Bloch space. We also improve some results of Dyakonov on the subject regarding Lipschitz spaces and Besov spaces. We present the results from the analysis of a diffractive element with a quasi-periodic structure of phyllotaxis type. The output pattern obtained from such a diffractive element is characterized by an annular symmetry that can be used in different applications. We discuss the influence of the parameters defining the diffractive element geometry on the diffracted pattern, showing that the golden angle interval is optimal for an arrangement of circular elements. We also demonstrate that the properties of the diffraction pattern can be changed by using proper non-binary phase functions for the diffractive element to obtain a non-symmetrical pattern, to reduce Ray Ban AAA Sunglasses Cream Pattern Black Rayban-0323 the zero order or to increase the intensity in a specific diffraction order.