Representation of Reproducing Kernels and the Lebesgue Constants on the Ball

Reproducing Kernels and Lebesgue Constants

Some Properties of Reproducing Kernel Banach and Hilbert Spaces

This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular, we try to extend this concept and prove some related theorems. Moreover, we focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular, we extend reproducing kernels to relative reproducing kernels an...

A Note on Solving Prandtl's Integro-Differential Equation

A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its ...

HILBERT SPACES OF TENSOR-VALUED HOLOMORPHIC FUNCTIONS ON THE UNIT BALL OF Cn

The expansion of reproducing kernels of Bergman spaces of holomorphic functions on a domain D in Cn is of considerable interests. If the domain admits an action of a compact group K, then naturally one would like to decompose the space of polynomials into irreducible subspaces of K and expand the reproducing kernels in terms of the reproducing kernels of the finite dimensional subspaces. In [5]...

An ‎E‎ffective Numerical Technique for Solving Second Order Linear Two-Point Boundary Value Problems with Deviating Argument

Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some n...