We prove new kernel theorems for a general class of Beurling-Björck type spaces. In particular, our results cover the classical spaces S(η)(ω) and S{η}{ω} defined via weight functions ω η.

An interesting and recently much studied generalization of the classical Schur class is the class of contractive operator-valued multipliers S(λ) for the reproducing kernel Hilbert space H(kd) on the unit ball B d ⊂ C, where kd is the positive kernel kd(λ,ζ) = 1/(1 − 〈λ, ζ〉) on B . The reproducing kernel space H(KS) associated with the positive kernel KS(λ,ζ) = (I −S(λ)S(ζ)∗) · kd(λ,ζ) is a nat...

There has been growing interest in kernel methods for classification, clustering and dimension reduction. For example, kernel Fisher discriminant analysis, spectral clustering and kernel principal component analysis are widely used in statistical learning and data mining applications. The empirical success of the kernel method is generally attributed to nonlinear feature mapping induced by the ...

The intersection of all two-sided ideals of an ordered semigroup, if it is non-empty, is called the kernel of the ordered semigroup. A left ideal L of an ordered semigroup (S, ·,≤) having a kernel I is said to be simple if I is properly contained in L and for any left ideal L′ of (S, ·,≤), I is properly contained in L′ and L′ is contained in L imply L′ = L. The notions of simple right and two-s...

We give a description of the kernel of the induction map K0(R) → K0(S), where S is a commutative ring and R = S G is the ring of invariants of the action of a finite group G on S. The description is in terms of H(G,GL(S)).

The goal of the spin foam approach 1 is to construct a mathematically well defined notion of path integral for non-perturbative quantum GR as a devise for computing the ‘dynamics’ of the theory. By ‘dynamics’ here we mean the characterization of the kernel of the quantum constraints given by the representation of the classical constraints in connection variables, schematically, Gi = DaE a i , V...

We give the first algorithm for kernel Nyström approximation that runs in linear time in the number of training points and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions. The algorithm projects the kernel onto a set of s landmark points sampled by their ridge leverage scores, requiring just O(ns) kernel evaluations and O(ns) additional r...

We study the kernels Kn,s(z) in the remainder terms Rn,s(f) of the Gauss-Turán quadrature formulae for analytic functions on elliptical contours with foci at ±1, when the weight ω is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel |Kn,s(z)| attains its maximum on the real axis (positive real semi...

In this work, we address the problem of protein-protein interaction network inference as a semi-supervised output kernel learning problem. Using the kernel trick in the output space allows one to reduce the problem of learning from pairs to learning a single variable function with values in a Hilbert space. We turn to the Reproducing Kernel Hilbert Space theory devoted to vectorvalued functions...

A direct implementation of the bilateral filter requires O(σ(s)(2)) operations per pixel, where σ(s) is the (effective) width of the spatial kernel. A fast implementation of the bilateral filter that required O(1) operations per pixel with respect to σ(s) was recently proposed. This was done by using trigonometric functions for the range kernel of the bilateral filter, and by exploiting t...