Related papers: On the extension of positive definite kernels to t…

Let E be a locally solid vector lattice. In this paper, we consider two particular vector subspaces of the space of all order bounded operators on E. With the aid of two appropriate topologies, we show that under some conditions, they…

We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…

We introduce the concept of linear topological modules over vertex algebras and apply it to representations of $\beta-\gamma$ system and affine Kac-Moody algebras.

We characterize bounded and compact positive Toeplitz operators defined on the Bergman spaces over the Siegel upper half-space.

Let $\Omega\subset\mathbb{R}^n$ be an open, connected subset of $\mathbb{R}^n$, and let $F\colon\Omega-\Omega\to\mathbb{C}$, where $\Omega-\Omega=\{x-y\colon x,y\in\Omega\}$, be a continuous positive definite function. We give necessary and…

We investigate the interaction between the existence of reproducing kernels on infinite-dimensional Hermitian vector bundles and the positivity properties of the corresponding bundles. The positivity refers to the curvature form of certain…

We establish the exponential law for suitably topologies on spaces of vector-valued smooth functions on topological groups, where smoothness is defined by using differentiability along continuous one-parameter subgroups. As an application,…

The theory of Toeplitz quantization presented in our previous paper is extended and further developed to include diverse and interesting non-commutative realizations of the classical Euclidean plane. This is done using Hilbert spaces of…

In view of recent developments of the study of reproducing kernel Hilbert spaces, in particular with the context the Hardy spaces on tubes, aspects of rational approximation for functions of finite energy in several complex and several real…

This note characterizes multiplicative linear functionals on reproducing kernel Hilbert spaces of functions on the Euclidean unit ball in complex d-dimensional space, in terms of their action on kernel functions. The kernels considered are…

We will remark an extension of a linear functional on subalgebra of algebra of continuous functions on subset of $\mathbb{R}^n$ which preserves positivity.

Vertex algebras provide an axiomatic algebraic description of the operator product expansion (OPE) of chiral fields in 2-dimensional conformal field theory. Vertex Lie algebras (= Lie conformal algebras) encode the singular part of the OPE,…

This paper is the first in a series of papers developing a functional-analytic theory of vertex (operator) algebras and their representations. For an arbitrary Z-graded finitely-generated vertex algebra (V, Y, 1) satisfying the standard…

In this paper, we specify what functions induce the bounded composition operators on a reproducing kernel Hilbert space (RKHS) associated with an analytic positive definite function defined on $\mathbf{R}^d$. We prove that only affine…

We shall generalize the notion of a Laver table to algebras which may have many generators, several fundamental operations, fundamental operations of arity higher than 2, and to algebras where only some of the operations are…

We study maximal representations of nonnegative sesquilinear forms in real or complex Hilbert spaces, that are not necessarily closed or even closable. We associate positive self-adjoint operators with such forms, in a sense similar to…

We describe conditions that characterize amenability for groups in terms of positive definite functions valued in a von Neumann algebra.

We show that any function in a Bergman space with exponential type weights admits a representation in terms of an infinite series of kernel functions.

We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their…

We introduce an asymptotic notion of positivity in algebraic geometry that turns out to be related to some high-dimensional convex sets. The dimension of the convex sets grows with the number of birational operations. In the case of complex…