Cross products of complete orthonormal systems of functions

S. V. Zotikov

Moscow State Pedagogical Correspondence Institute

Abstract: The orthonormal kernel is a continuous analog for an orthonormal system of functions. The cross product of any two orthonormal systems, complete in $L_2$, 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 $L_2$, and totally bounded. We investigate certain properties of the cross product of a Haar system with another Haar system.

UDC: 517.5

Received: 10.04.1973

 English version: Mathematical Notes, 1974, 15:2, 187–191

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