Cross products of complete orthonormal systems of functions

Abstract

The orthonormal kernel is a continuous analog for an orthonormal system of functions. The cross product of any two orthonormal systems, complete in L2, is an example of a complete orthonormal kernel with respect to Lebesgue measure. In this note we continue our study of the properties of the cross product of a Haar system with an arbitrary orthonormal system of functions, complete in L2, and totally bounded. We investigate certain properties of the cross product of a Haar system with another Haar system.