GRAMIAN ORTHOGONALLY SCATTERED DILATION OF -VALUED MEASURES WITH APPLICATIONS

L-orthogonally scattered measures

Scattered manifold-valued data approximation

We consider the problem of approximating a function f from an Euclidean domain to a manifold M by scattered samples [Formula: see text], where the data sites [Formula: see text] are assumed to be locally close but can otherwise be far apart points scattered throughout the domain. We introduce a natural approximant based on combining the moving least square method and the Karcher mean. We prove ...

Integration with Respect to Operator-Valued Measures with Applications to Quantum Estimation Theory (*)(**)

This paper is concerned with the development of an integration theory with respect to operator-valued measures which is required in the study o/ certain convex optimization problems. These convex optimization problems in their turn are rigorous ]ormulations o] detection theory in a quantum communication context, which generalise classical (Bayesian) detection theory. The integration theory whic...

Interval-Valued Probability Measures

The purpose of this paper is propose a simple de…nition of an interval-valued probability measure and to examine some of the implications of this de…nition. This de…nition provides a method for characterizing certain types of imprecise probabilities. We develop some properties of this de…nition and propose a de…nition of integration with respect to it. We show that this de…nition is a generaliz...

Modulus of Lattice-valued Measures

Let X be a completely regular Hausdorff space, E a Banach lattice, and μ an E-valued countably additive, regular Borel measure on X. Some results about the countable additivity and regularity of the modulus |μ| are proved. Also in special cases, it is proved that L1(μ) = L1(|μ|).