Related papers: Highly localized kernels on space of homogeneous t…

We study the orthogonal projection of homogeneous polynomials onto the space of homogeneous polyharmonic polynomials. To do this we derive the decomposition of homogeneous polynomials in terms of the Kelvin transform of derivatives of the…

One deals with arbitrary reduced free divisors in a polynomial ring over a field of characteristic zero, by stressing the ideal theoretic and homological behavior of the corresponding singular locus. A particular emphasis is given to both…

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 describe the Bergman kernel of any bounded homogeneous domain in a minimal realization relating to the Bergman kernels of the Siegel disks. Taking advantage of this expression, we obtain substantial estimates of the Bergman kernel of the…

For any smooth projective variety with holomorphic locally homogeneous structure modelled on a homogeneous algebraic variety, we determine all the subvarieties of it which develop to the model.

Orthogonal polynomials for the multivariate hypergeometric distribution are defined on lattices in polyhedral domains in $\RR^d$. Their structures are studied through a detailed analysis of classical Hahn polynomials with negative integer…

We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, homogeneous kernels of such operators are also studied. The…

In this paper we study continuous kernels on compact two point homogeneous spaces which are positive definite and zonal (isotropic). Such kernels were characterized by R. Gangolli some forty years ago and are very useful for solving…

This paper proposes a general machine learning framework called the localization method, which is fundamentally built on two core concepts: localization kernels and local means -- key components that underpin the self-attention mechanism.…

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

We study the logarithmic topological Hochschild homology of ring spectra with logarithmic structures and establish localization sequences for this theory. Our results apply, for example, to connective covers of periodic ring spectra like…

The notion of a flag kernel on a homogeneous group is exteded to distributions of arbitrary multidimensional order. It is shown that under natural restrictions on order the operation of convolution admits an extension to thus generalised…

In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…

We present new classes of positive definite kernels on non-standard spaces that are integrally strictly positive definite or characteristic. In particular, we discuss radial kernels on separable Hilbert spaces, and introduce broad classes…

We define homogeneous principal Higgs and co-Higgs bundles over irreducible Hermitian symmetric spaces of compact type. We provide a classification for each type of object up to isomorphism, which in each case can be interpreted as defining…

This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…

We define a family of kernels for mixed continuous/discrete hierarchical parameter spaces and show that they are positive definite.

Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…

The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…

Recently, many works focus on the implementation of collective communication operations adapted to wide area computational systems, like computational Grids or global-computing. Due to the inherently heterogeneity of such environments, most…