Related papers: Negative definite functions and a dynamical charac…
We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest,…
A new definition of random sets is proposed. It is based on the distance in measurable space and uses negative definite kernels for continuation from initial space to that of random sets. This approach has no connection to Hausdorff…
We classify finite groups $G$, such that the group algebra, $\mathbb{Q}G$ (over the field of rational numbers $\mathbb{Q}$), is the direct product of the group algebra $\mathbb{Q}[G/N]$ of a proper factor group $G/N$, and some division…
We define and study entanglement of continuous positive definite functions on products of compact groups. We formulate and prove an infinite-dimensional analog of Horodecki Theorem, giving a necessary and sufficient criterion for…
Let $S$ be a subset of a amenable group $G$ such that $e\in S$ and $S^{-1}=S$. The main result of the paper states that if the Cayley graph of $G$ with respect to $S$ has a certain combinatorial property, then every positive definite…
Magnitude is a numerical invariant of finite metric spaces, recently introduced by T. Leinster, which is analogous in precise senses to the cardinality of finite sets or the Euler characteristic of topological spaces. It has been extended…
We introduce a natural concept of positive definiteness for bundle maps between Fell bundles over (possibly different) discrete groups and describe several examples. Such maps induce completely positive maps between the associated full…
We give the definition of an invariant random positive definite function on a discrete group, generalizing both the notion of an invariant random subgroup and a character. We use von Neumann algebras to show that all invariant random…
We show that, for positive definite kernels, if specific forms of regularity (continuity, Sn-differentiability or holomorphy) hold locally on the diagonal, then they must hold globally on the whole domain of positive-definiteness. This…
Let $X$ be a set and let $S$ be an inverse semigroup of partial bijections of $X$. Thus, an element of $S$ is a bijection between two subsets of $X$, and the set $S$ is required to be closed under the operations of taking inverses and…
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…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in…
The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes. Letting a function act by post composition on kernels with arbitrary domains, it is shown…
We present a characterization for a positive definite operator valued kernel to be universal or $C_{0}$-universal, and apply these characterizations to a family of operator valued kernels that are shown to be well behaved. Later, we obtain…
In this paper we investigate the class of invariant positive definite kernels on the free semigroup on N generators. We provide a combinatorial description of the positivity of the kernel in terms of Dyck paths and then we find a…
The class of uniformly computable real functions with respect to a small subrecursive class of operators computes the elementary functions of calculus, restricted to compact subsets of their domains. The class of conditionally computable…
In this paper, we study the coarse kernel of a group action, namely the normal subgroup of elements that translate every point by a uniformly bounded amount. We give a complete algebraic characterization of this object. We specialize to…
A sequence of non-negative integers is exactly realizable as the fixed point counts sequence of a dynamical system if and only if it gives rise to a sequence of non-negative orbit counts. This provides a simple realizability criterion based…
Godel's theory T can be understood as a theory of the simply-typed lambda calculus that is extended to include the constant 0, the successor function S, and the operator R_tau for primitive recursion on objects of type tau. It is known that…
The author was recently able to provide a cohomological interpretation of Tate's Riemann-Roch formula for number fields using some new harmonic analysis objects, ghost-spaces. When trying to investigate these objects in general, we realized…