Cross products of complete orthonormal systems of functions

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.Translated from Matematicheskie Zametki, Vol. 15, No. 2, pp. 331–340, February, 1974.The author thanks Professor N. Ya. Vilenkin for helpful discussions during the course of this work.