The L-cosine transform of an even, continuous function f ∈ Ce(S ) is defined by: H(x) = ∫ S |〈x, ξ〉|f(ξ) dξ, x ∈ R. It is shown that if p is not an even integer then all partial derivatives of even order of H(x) up to order p + 1 (including p + 1 if p is an odd integer) exist and are continuous everywhere in R\{0}. As a result of the corresponding differentiation formula, we show that if f is a...

Motivated by the study of autoequivalence group triangulated categories via isometric actions on metric spaces, we consider curvature properties (CAT(0), Gromov hyperbolic) space Bridgeland stability conditions with canonical defined Bridgeland. We then prove that is neither CAT(0) nor hyperbolic, and quotient natural $${\mathbb C}$$ -action not in case Kronecker quiver. Moreover, also show hyp...

Firstly, two new kinds of Kronecker decompositions is developed, i.e. KPGD and KPID; Secondly, the sufficient and necessary conditions and algorithms of Kronecker product(KPD), KPGD, and KPID are discussed; At last, some useful properties of the rank of the sum of Kronecker product gemel decompositions are obtained.

LetK be a d-dimensional convex bodywith a twice continuously differentiable boundary and everywhere positive Gauss–Kronecker curvature. Denote byKn the convex hull of n points chosen randomly and independently fromK according to the uniform distribution. Matching lower andupper bounds are obtained for the orders ofmagnitudeof the variances of the sth intrinsic volumes Vs(Kn) of Kn for s ∈ {1, ....

In this paper we define ?-independent (a weak-version of independence), Kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and Sidon sets. These sets have the lacunarity or thinness property and are very useful indeed. For example Varopoulos used the Kronecker sets to prove the Malliavin theorem. In t...

We saw in Lecture 3 how to efficiently multiply integers, and, using Kronecker substitution, how to efficiently multiply polynomials with integer coefficients. This gives us what we need to multiply elements in finite fields, provided that we have a way to reduce the result to our standard representations of Fp ' Z/pZ and Fq ' Fp[x]/(f), using integers in [0, p− 1] and polynomials of degree les...

We give several new algorithms for dense polynomial multiplication based on the Kronecker substitution method. For moderately sized input polynomials, the new algorithms improve on the performance of the standard Kronecker substitution by a sizeable constant, both in theory and in empirical tests.

Translated into the language of representations of quivers, a challenge in matrix pencil theory is to find sufficient and necessary conditions for a Kronecker representation to be a subfactor of another Kronecker representation in terms of their Kronecker invariants. The problem is reduced to a numerical criterion for a Kronecker representation to be a subrepresentation of another Kronecker rep...