Related papers: Which Spaces can be Embedded in Reproducing Kernel…

Generalizing previous work of Iwaniec, Luo, and Sarnak (2000), we use information from one-level density theorems to estimate the proportion of non-vanishing of $L$-functions in a family at a low-lying height on the critical line (measured…

We prove that a Hilbert space frame $\fti$ contains a Riesz basis if every subfamily $\ftj , J \subseteq I ,$ is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic…

Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…

In this paper we study embeddings between de Branges-Rovnyak spaces $H(b)$ and harmonically weighted Dirichlet spaces $\mathcal{D}(\mu)$ in terms of the boundary spectrum of $b$ and the support of the measure $\mu$, by using elementary…

Let $E$, $F$ be separable Hilbert spaces, and assume that $E$ is infinite-dimensional. We show that for every continuous mapping $f:E\to F$ and every continuous function $\varepsilon: E\to (0, \infty)$ there exists a $C^{\infty}$ mapping…

In this paper we analyse the structure of the spaces of smooth type functions, generated by elements of arbitrary Hilbert spaces, as a continuation of the research in our previous papers in this series. We prove that these spaces are…

For a bounded linear operator $T$ acting on a reproducing kernel Hilbert space $\mathcal{H}(\Omega)$ over some non-empty set $\Omega$, the Berezin range and the Berezin radius of $T$ are defined respectively, by $\text{Ber}(T) := \{\langle…

This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of…

Let $A$ be a set and $V$ a real Hilbert space. Let $H$ be a real Hilbert space of functions $f:A\to V$ and assume $H$ is continuously embedded in the Banach space of bounded functions. For $i=1,\cdots,n$, let $(x_i,y_i)\in A\times V$…

Recently, there has been growing interest in characterizing the function spaces underlying neural networks. While shallow and deep scalar-valued neural networks have been linked to scalar-valued reproducing kernel Banach spaces (RKBS),…

We introduce a complex-valued counterpart of the representer theorem in machine learning. We study several learning and minimization problems in reproducing kernel Hilbert spaces (RKHSs), with the aim of identifying appropriate input-output…

Universal kernels, whose Reproducing Kernel Hilbert Space is dense in the space of continuous functions are of great practical and theoretical interest. In this paper, we introduce an explicit construction of universal kernels on compact…

We study the boundedness of composition operators on the bidisk using reproducing kernels. We show that a composition operator is bounded on the Hardy space of the bidisk if some associated function is a positive kernel. This positivity…

We give an elementary construction of representing systems of the Cauchy kernels in the Hardy spaces $H^p$, $1 \le p <\infty$, as well as of representing systems of reproducing kernels in weighted Hardy spaces.

We obtain two results concerning the Feichtinger conjecture for systems of normalized reproducing kernels in the model subspace $K_\Theta = H^2\ominus \Theta H^2$ of the Hardy space $H^2$, where $\Theta$ is an inner function. First, we…

In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output…

This paper ist concerned with recent progress in the context of coorbit space theory. Based on a square integrable group representation, the coorbit theory provides new families of associated smoothness spaces, where the smoothness of a…

We find probability error bounds for approximations of functions $f$ in a separable reproducing kernel Hilbert space $\mathcal{H}$ with reproducing kernel $K$ on a base space $X$, firstly in terms of finite linear combinations of functions…

The bicomplex Bergman spaces are studied for any bounded bicomplex domain. Its Bergman kernel is computed in terms of the kernels of the complex projections of the domain. We also introduce two additional reproducing kernel Hilbert spaces…

This paper discusses the convexity of the range of the Berezin transform. For a bounded operator $T$ acting on a reproducing kernel Hilbert space $H$ (on a set $X$), this is the set $B(T) : = \{ < Tk_x, k_x >_H : x \in X \}$, where $k_x$ is…