The theory of reproducing kernels started with two papers of 1921 [449] and 1922 [45] which
dealt with typical reproducing kernels of Szegö and Bergman, and since then the theory has …

Abstract Let Y={f (i), Af (i),…, A lif (i): i∈ Ω}, where A is a bounded operator on ℓ 2 (I). The
problem under consideration is to find necessary and sufficient conditions on A, Ω,{li: i∈ Ω} …

Let A be a normal operator in a Hilbert space H, and let G⊂ H be a countable set of vectors.
We investigate the relations between A, G and L that make the system of iterations {A ng: g∈ …

Recently, there has been emerging interest in constructing reproducing kernel Banach
spaces (RKBS) for applied and theoretical purposes such as machine learning, sampling …

A spatially distributed network contains a large amount of agents with limited sensing, data
processing, and communication capabilities. Recent technological advances have opened …

Asymmetric kernels naturally exist in real life, eg, for conditional probability and directed
graphs. However, most of the existing kernel-based learning methods require kernels to be …

In industry and economics, the most common solutions of partial differential equations
involving multivariate numerical integration over cuboids include techniques of iterated one …

In this paper, we study random sampling in a reproducing kernel space V, which is the range
of an idempotent integral operator. Under certain decay condition on the integral kernel, we …

The objective of sampling in Euclidean spaces is to deal with the reconstruction of a
(bandlimited) function (or more generally by a function in an appropriate Hilbert space) by …

In this paper, we consider (random) sampling of signals concentrated on a bounded
Corkscrew domain Ω of a metric measure space, and reconstructing concentrated signals …