Refined Kato inequalities in riemannian geometry

A Geometry Preserving Kernel over Riemannian Manifolds

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

Riemannian geometry

Collapse in Riemannian Geometry

Refined Convex Sobolev Inequalities

This paper is devoted to refinements of convex Sobolev inequalities in the case of power law relative entropies: a nonlinear entropy–entropy production relation improves the known inequalities of this type. The corresponding generalized Poincaré type inequalities with weights are derived. Optimal constants are compared to the usual Poincaré constant.

On Temple–kato like Inequalities and Applications

The so called Wilkinson’s Schur complement trick plays a prominent role in the theory of eigenvalue estimates for finite matrices. We apply this technique to the problem of obtaining Ritz value spectral estimates for a positive definite self-adjoint operator in a Hilbert space. New estimates have a form of a Temple–Kato like inequality and are particularly suited to a situation in which we are ...