Related papers: Reproducing kernels of some weighted Bergman space…

In this work we solve a degenerate parabolic equation for the half line with Dirichlet boundary data, and use some results from the theory of Reproducing Kernel Hilbert Spaces to show that the null reachable space of this degenerate…

We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

In this paper, we give some results concerning atomic decompositions for operators on reproducing kernel Hilbert spaces, using frame theory techniques. We provide also generalizations for atomic decompositions of some theorems for…

We find kernel functions of the $q$-Heun equation and its variants. We apply them to obtain $q$-integral transformations of solutions to the $q$-Heun equation and its variants. We discuss special solutions of the $q$-Heun equation from the…

We develop sampling formulas for high-dimensional functions in reproducing kernel Hilbert spaces, where we rely on irregular samples that are taken at determining sequences of data points. We place particular emphasis on sampling formulas…

For $1<p<\infty$, we emulate the Bergman projection on Reinhardt domains by using a Banach-space basis of $L^p$-Bergman space. The construction gives an integral kernel generalizing the ($L^2$) Bergman kernel. The operator defined by the…

We construct a bounded plane domain which is Bergman complete but for which the Bergman kernel does not tend to infinity as the point approaches the boundary.

We shall give an explicit estimate of the lower bound of the Bergman kernel associated to a positive line bundle. In the compact Riemann surface case, our result can be seen as an explicit version of Tian's partial $C^0$-estimate.

In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for intersection of two complex ellipsoids $\{z \in \mathbb{C}^3 \colon |z_1|^p +…

Kernels for structured data are commonly obtained by decomposing objects into their parts and adding up the similarities between all pairs of parts measured by a base kernel. Assignment kernels are based on an optimal bijection between the…

In this paper, we give a new approach to the theory of strictly positive kernels. Our method is based on the structure of Fock spaces. As its applications, various examples of strictly positive kernels are given. Moreover, we give a new…

We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…

We give a proof that every space of weighted square-integrable holomorphic functions admits an equivalent weight whose Bergman kernel has zeroes. Here the weights are equivalent in the sense that they determine the same space of holomorphic…

We prove two theorems of Paley and Wiener in the slice regular setting. As an application, we can compute the reproducing kernel for the slice regular Paley-Wiener space, and obtain a related sampling theorem.

We produce precise estimates for the Kogbetliantz kernel for the approximation of functions on the sphere. Furthermore, we propose and study a new approximation kernel, which has slightly better properties.

We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a…

In this paper, we investigate a restricted version of Bergman kernels for high powers of a big line bundle over a smooth projective variety. The geometric meaning of the leading term is specified. As a byproduct, we derive some integral…