The purpose of this paper is to discuss the degree best monotone multi- approximation unbounded functions weighted space in terms modules smoothness by using some algebraic linear operators. In addition, introduced ,proofs properties modulus smoothness.

Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcal{H}(Omega_X)$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcal{A}^omega(Omega_X)$ is the space of all $finmathcal{H}(Omega_X)$ for which $$|f(x)|leqslant C omega(r_{Omega_X}(x)),quad xin Omega_X,$$ for some constant $C>0$, whenever $r_{Omega_X}$ is the M...

Starting with a general formula, precise but difficult to use, for the adjoint of a composition operator on a functional Hilbert space, we compute an explicit formula on the classical Hardy Hilbert space for the adjoint of a composition operator with rational symbol. To provide a foundation for this formula, we study an extension to the definitions of composition, weighted composition, and Toep...

We study the symplectic geometry of the moduli spaces Mr = Mr(H ) of closed n-gons with fixed side-lengths in hyperbolic three-space. We prove that these moduli spaces have almost canonical symplectic structures. They are the symplectic quotients of B by the dressing action of SU(2) (here B is the standard Borel subgroup of SL2(C)). We show that the hyperbolic Gauss map sets up a real analytic ...

Let be weighted Bergman space on a bounded symmetric domain . It has analytic continuation in the weight and for in the so-called Wallach set still forms unitary irreducible (projective) representations of . We give the irreducible decomposition of the tensor product of the representation for any two unitary weights and we find the highest weight vectors of the irreducible components. We find a...

We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H1 space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within ε of a stable profile, then the unique solution of the C...

We study the symplectic geometry of the moduli spaces Mr = Mr(H ) of closed n-gons with fixed side-lengths in hyperbolic three-space. We prove that these moduli spaces have almost canonical symplectic structures. They are the symplectic quotients of B by the dressing action of SU(2) (here B is the subgroup of the Borel subgroup of SL2(C) defined below). We show that the hyperbolic Gauss map set...

We study the symplectic geometry of the moduli spaces Mr = Mr(H) of closed n-gons with fixed side-lengths in hyperbolic three-space. We prove that these moduli spaces have almost canonical symplectic structures. They are the symplectic quotients of Bn by the dressing action of SU(2) (here B is the subgroup of the Borel subgroup of SL2(C) defined below). We show that the hyperbolic Gauss map set...

In this work we consider quasi-optimal versions of the Stochastic Galerkin Method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the solution of the PDE with respect to the parameters in a polydisc of the complex plane C . We show that a quasi-optimal approximation is given by...