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Matematicheskie Zametki, 1974, Volume 15, Issue 2, Pages 331–340 (Mi mzm7353)  
Cross products of complete orthonormal systems of functions

S. V. Zotikov

Moscow State Pedagogical Correspondence Institute
Full-text PDF (595 kB)
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.
Received: 10.04.1973
English version:
Mathematical Notes, 1974, Volume 15, Issue 2, Pages 187–191
DOI: https://doi.org/10.1007/BF02102405
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: S. V. Zotikov, “Cross products of complete orthonormal systems of functions”, Mat. Zametki, 15:2 (1974), 331–340; Math. Notes, 15:2 (1974), 187–191
Citation in format AMSBIB
\Bibitem{Zot74}
\by S.~V.~Zotikov
\paper Cross products of complete orthonormal systems of functions
\jour Mat. Zametki
\yr 1974
\vol 15
\issue 2
\pages 331--340
\mathnet{http://mi.mathnet.ru/mzm7353}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=348390}
\zmath{https://zbmath.org/?q=an:0304.42018|0302.42015}
\transl
\jour Math. Notes
\yr 1974
\vol 15
\issue 2
\pages 187--191
\crossref{https://doi.org/10.1007/BF02102405}
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