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.
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N. Ya. Vilenkin and S. V. Zotikov, “The cross product of orthonormal systems of functions,” Matem. Zametki,13, No. 3, pp. 469–480 (1973).
N. I. Akhiezer, Lectures on the Theory of Approximation [in Russian], (1965).
P. L. Ul'yanov, “Series with respect to Haar systems,” Matem. Sbornik,63, No. 3, pp. 356–391 (1964).
G. Aleksich, Problems on the Convergence of Orthogonal Series [in Russian] (1963).
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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.
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Zotikov, S.V. Cross products of complete orthonormal systems of functions. Mathematical Notes of the Academy of Sciences of the USSR 15, 187–191 (1974). https://doi.org/10.1007/BF02102405
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DOI: https://doi.org/10.1007/BF02102405