Norm minima in certain Siegel leaves

Klein Polyhedra and Lattices with Positive Norm Minima

A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of R n. It generalizes the concept of continued fraction. In this paper facets and edge stars of vertices of a Klein polyhedron are considered as multidimensional analogs of partial quotients and quantitative characteristics of these " partial quotients " , so called determinants, are defined. It is pro...

Klein polyhedra and lattices with positive norm minima par

A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of R. It generalizes the concept of continued fraction. In this paper facets and edge stars of vertices of a Klein polyhedron are considered as multidimensional analogs of partial quotients and quantitative characteristics of these “partial quotients”, so called determinants, are defined. It is proved t...

Uniqueness of Minima of a Certain Least Squares Problem

This paper is essentially an exercise in studying the minima of a certain least squares optimization using the second partial derivative test. The motivation is to gain insight into an optimization-based solution to the problem of tracking human limbs using IMU sensors.

Existence of an Algebra Norm on Certain Subalgebras of C(X)

Mixed Norm Estimates for Certain Generalized Radon Transforms

In this paper we investigate the mapping properties in Lebesgue-type spaces of certain generalized Radon transforms defined by integration over curves. Let X and Y be open subsets of R, d ≥ 2, and let Z be a smooth submanifold of X×Y ⊂ R2d of dimension d+1. Assume that the projections π1 : Z → X and π2 : Z → Y are submersions at each point of Z. For each y ∈ Y , let γy = {x ∈ X : (x, y) ∈ Z} = ...