We perform a convergence analysis for discretization of Helmholtz scattering and resonance problems obtained by Hardy space infinite elements. Super-algebraic convergence with respect to the number of Hardy space degrees of freedom is achieved. As transparent boundary spheres and piecewise polytopes are considered. The analysis is based on a G̊arding-type inequality and standard operator theoret...

We consider Carleson measures, Hankel matrices, and interpolation of values on certain reproducing kernel Hilbert spaces which we call the diameter spaces. We begin by reviewing results for the classical Hardy space which we denote DAH1 and its associated diameter space. Our n−dimensional analog of the Hardy space is the Drury-Arveson-Hardy space, DAHn, a space of holomorphic functions on the u...

For a fixed nonnegative integer $m$, an analytic map $\varphi$ and function $\psi$, the generalized integration operator $I^{(m)}_{\varphi,\psi}$ is defined by \[ I^{(m)}_{\varphi,\psi} f(z) = \int_0^z f^{(m)}(\varphi(\zeta)) \psi(\zeta) \, d\zeta \] for $X$-valued $f$, where $X$ Banach space. Some estimates norm of $I^{(m)}_{\varphi,\psi} \colon wA^p_{\alpha}(X) \to A^p_{\alpha}(X)$ are obtain...

As new applications of Schrödinger type inequalities obtained by Jiang (J. Inequal. Appl. 2016: Article ID 247, 2016) in the Schrödingerean Hardy space, we not only obtain the representation of Schrödingerean harmonic functions but also give a sufficient and necessary condition between the Schrödingerean distributional function and its derivative in the Schrödingerean Hardy space.

In this paper, we introduce a new concept in set-valued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that ...

The semi-inner product, in the sense of Lumer, on weighted Hardy space which generate the norm is unique. Also we will discuss some properties of the numerical range of bounded linear operators on weighted Hardy spaces.

We prove an optimal Hardy inequality for the fractional Laplacian on the half-space. 1. Main result and discussion Let 0 < α < 2 and d = 1, 2, . . .. The purpose of this note is to prove the following Hardy-type inequality in the half-space D = {x = (x1, . . . , xd) ∈ R : xd > 0}. Theorem 1. For every u ∈ Cc(D), (1) 1 2 ∫

We give general estimates for the approximation numbers of composition operators on the Hardy space on the ball Bd and the polydisk D . Mathematics Subject Classification 2010. Primary: 47B33 – Secondary: 32A07 – 32A35 – 32A70 – 46E22 – 47B07 Key-words. approximation numbers; bounded symmetric domain; composition operator; Hardy space; polydisk; Reinhardt domain; several complex variables

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...