Approximation of monogenic functions by higher order Szegö kernels on the unit ball and half space
نویسنده
چکیده
We study the adaptive decomposition of functions in the monogenic Hardy spaces H2 by higher order Szegö kernels under the framework of Clifford algebra and Clifford analysis, in the context of unit ball and half space. This is a sequel and a higher-dimensional generalization of our recent study on the complex Hardy spaces.
منابع مشابه
Fekete-Szegö coefficient functional for transforms of universally prestarlike functions
Universally prestarlike functions of order $alphaleq 1$ in the slit domain $Lambda=mathbb{C}setminus [1,infty)$ have been recently introduced by S. Ruscheweyh.This notion generalizes the corresponding one for functions in the unit disk $Delta$ (and other circular domains in $mathbb{C}$). In this paper, we obtain the Fekete-Szegö coefficient functional for transforms of such f...
متن کاملA New Class of Spatial Covariance Functions Generated by Higher-order Kernels
Covariance functions and variograms play a fundamental role in exploratory analysis and statistical modelling of spatial and spatio-temporal datasets. In this paper, we construct a new class of spatial covariance functions using the Fourier transform of some higher-order kernels. Moreover, we extend this class of spatial covariance functions to the spatio-temporal setting using the idea used in...
متن کاملModuli of bounded holomorphic functions in the ball
We prove that there is a continuous non-negative function g on the unit sphere in C d, d ≥ 2, whose logarithm is integrable with respect to Lebesgue measure, and which vanishes at only one point, but such that no non-zero bounded analytic function m in the unit ball, with boundary values m⋆, has |m⋆| ≤ g almost everywhere. The proof analyzes the common range of co-analytic Toeplitz operators in...
متن کاملSOME REMARKS ON WEAKLY INVERTIBLE FUNCTIONS IN THE UNIT BALL AND POLYDISK
We will present an approach to deal with a problem of existence of (not) weakly invertible functions in various spaces of analytic functions in the unit ball and polydisk based on estimates for integral operators acting between functional classes of different dimensions.
متن کاملWeighted Approximation of Functions on the Unit Sphere
The direct and inverse theorems are established for the best approximation in the weighted L space on the unit sphere of R, in which the weight functions are invariant under finite reflection groups. The theorems are stated using a modulus of smoothness of higher order, which is proved to be equivalent to a K-functional defined using the power of the spherical h-Laplacian. Furthermore, similar ...
متن کامل