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A property of Haar’s system of orthogonal functions. (English) JFM 49.0293.02
Das von A. Haar in seiner Dissertation (Math. Ann. 69, 331; s. F. d. M. 41, 469, 1910) aufgestellte Orthogonalsystem soll durch die folgende Minimaleigenschaft charakterisiert werden: Die \((n+1)\)-te Funktion besitzt unter allen zu den ersten \(n\) Funktionen orthogonalen Funktionen vom Integralquadrat 1 die kleinste totale Variation. Es wird gezeigt, daß das Haarsche System diese Eigenschaft besitzt.

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References:
[1] Mathematische Annalen69 (1910), S. 331-371.
[2] Either or both of these may be limits to the right or to the left; thus the former may be subject to the restrictionx>a orx<a.
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