相关论文: Strictly Positive Definite Functions on Compact Tw…

We study positive kernels on $X\times X$, where $X$ is a set equipped with an action of a group, and taking values in the set of $\mathcal A$-sesquilinear forms on a (not necessarily Hilbert) module over a $C^*$-algebra $\mathcal A$. These…

This paper considers the properties of Dirichlet Spaces of Homogeneous type which consist of band limited functions that are nearly exponential localizations on $\mathbb{R}^k.$ This is a powerful tool in harmonic analysis and it makes…

Let $G$ be a compact Lie group acting isometrically on a compact Riemannian manifold $M$ with nonempty fixed point set $M^G$. We say that $M$ is fixed-point homogeneous if $G$ acts transitively on a normal sphere to some component of $M^G$.…

We prove that two homogeneous ultra-metric spaces $X,Y$ are coarsely equivalent if and only if $\mathrm{Ent}^\sharp(X)=\mathrm{Ent}^\sharp(Y)$ where $\mathrm{Ent}^\sharp(X)$ is the so-called sharp entropy of $X$. This classification implies…

It has been shown that the maximum stable set problem in some infinite graphs, and the kissing number problem in particular, reduces to a minimization problem over the cone of copositive kernels. Optimizing over this infinite dimensional…

With view to applications in stochastic analysis and geometry, we introduce a new correspondence for positive definite kernels (p.d.) $K$ and their associated reproducing kernel Hilbert spaces. With this we establish two kinds of…

This note consists of two largely independent parts. In the first part we give conditions on the kernel $k: \Omega \times \Omega \rightarrow \mathbb{R}$ of a reproducing kernel Hilbert space $H$ continuously embedded via the identity…

Using the formalism of quantizers and dequantizers, we show that the characters of irreducible unitary representations of finite and compact groups provide kernels for star products of complex-valued functions of the group elements.…

The aim of this paper is to continue the study of sg-compact spaces. The class of sg-compact spaces is a proper subclass of the class of hereditarily compact spaces. In our paper we shall consider sg-compactness in product spaces. Our main…

This work presents a rigorous characterization of inner products on the Hilbert space $S_2$ of Hilbert--Schmidt operators. We first deal with a general setting of continuous sesquilinear forms on a Hilbert space $\mathcal H$, and provide a…

The main aim of the paper is to give a full classification (up to isometry) of all metric spaces X with the following two properties: X contains a compact set with non-empty interior; and for any three distinct points a, b and c of X there…

We prove genuinely sharp two-sided global estimates for heat kernels on all compact rank-one symmetric spaces. This generalizes the authors' recent result obtained for a Euclidean sphere of arbitrary dimension. Furthermore, similar heat…

Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of…

Several characterizations are given for a square matrix that can be written as the product of two positive (semidefinite) projections. Based on one of these characterizations, and the theory of alternating projections, a Matlab program is…

Consider a compact Lie group $G$ and a closed subgroup $H<G$. Suppose $\mathcal M$ is the set of $G$-invariant Riemannian metrics on the homogeneous space $M=G/H$. We obtain a sufficient condition for the existence of $g\in\mathcal M$ and…

The main aim of this article is to establish boundedness of singular integrals with non-smooth kernels on product spaces. Let $L_1$ and $L_2$ be non-negative self-adjoint operators on $L^2(\mathbb{R}^{n_1})$ and $L^2(\mathbb{R}^{n_2})$,…

In this note we give a recursive formula for the derivatives of isotropic positive definite functions on the Hilbert sphere. We then use it to prove a conjecture stated by Tr\"ubner and Ziegel, which says that for a positive definite…

In this paper we generalize Wiener's characterization of continuous measures to compact homogenous manifolds. In particular, we give necessary and sufficient conditions on probability measures on compact semisimple Lie groups and…

For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…

We construct a large family of positive-definite kernels $K: \mathbb{D}^n\times \mathbb{D}^n \to \mbox{M} (r, \mathbb C)$, holomorphic in the first variable and anti-holomorphic in the second, that are quasi-invariant with respect to the…