Related papers: Generalized de Branges-Rovnyak spaces
We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are…
In this paper, we study the de Branges-Rovnyak spaces $\mathcal{H}(B)$ generated by row Schur functions $B$ with mate $a$. We prove that the polynomials are dense in $\mathcal{H}(B)$, and characterize the backward shift invariant subspaces…
This paper focuses on representations of contractively embedded invariant subspaces in several variables. We present a version of the de Branges theorem for $n$-tuples of multiplication operators by the coordinate functions on analytic…
We exhibit three classes of compactly supported functions which provide reproducing kernels for the Sobolev spaces $H^\delta(\R^d)$ of arbitrary order $\,\delta>d/2.\,$ Our method of construction is based on a new class of oscillatory…
Recently, there has been emerging interest in constructing reproducing kernel Banach spaces (RKBS) for applied and theoretical purposes such as machine learning, sampling reconstruction, sparse approximation and functional analysis.…
This article is concerned with an approximate analytical solution for the time fractional Kudryashov Sinelshchikov equation by using the reproducing kernel Hilbert space method. The main tools of this method are reproducing kernel theory,…
We study the elastic Herglotz wave functions, which are entire solutions of the spectral Navier equation appearing in the linearized elasticity theory with $L^2-$far-field patterns. We characterize in three-dimensions the set of these…
In this paper, we illustrate the effectiveness of reproducing kernel Hilbert space techniques in the study of composition operators. For weighted Hardy spaces on the unit disk, we characterize the composition operators whose adjoint is…
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…
This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…
In this paper we introduce a reproducing kernel Hilbert space defined on $\mathbb{R}^{d+1}$ as the tensor product of a reproducing kernel defined on the unit sphere $\mathbb{S}^{d}$ in $\mathbb{R}^{d+1}$ and a reproducing kernel defined on…
This study shows how Aronszajn's theory of reproducing kernels can be of use for the construction the Hilbert spaces of quantum theory. We show that the Feynman propagator is an example of a reproducing kernel under a boundedness condition.…
Various convergence results for the Bergman kernel of the Hilbert space of all polynomials in \C^{n} of total degree at most k, equipped with a weighted norm, are obtained. The weight function is assumed to be C^{1,1}, i.e. it is…
Indefinite inner product spaces of entire functions and functions analytic inside a disk are considered and their completeness studied. Spaces induced by the rotation invariant reproducing kernels in the form of the generalized…
Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view…
We suppose that $G$ is a locally compact abelian group, $Y$ is a measure space, and $H$ is a reproducing kernel Hilbert space on $G\times Y$ such that $H$ is naturally embedded into $L^2(G\times Y)$ and it is invariant under the…
In this note, we compute the reproducing kernel for the RKHS of functions on $\mathbb{R}^n$ in a sufficiently high Sobolev norm.
Using an explicit construction, we show that the de Branges-Rovnyak spaces $\mathscr{H}(b)$, corresponding to rational $b$, are contained in their associated Smirnov classes.
We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive…
We prove a characterization for the Peetre type $K$-functional on $\mathbb{M}$, a compact two-point homogeneous space, in terms the rate of approximation of a family of multipliers operator defined to this purpose. This extends the well…