Transactions of the American Mathematical Society

Some ramifications of a theorem of Boas and Pollard concerning the completion of a set of functions in $L^{2}$

Author(s): K. S. Kazarian; Robert E. Zink
Journal: Trans. Amer. Math. Soc. 349 (1997), 4367-4383.
MSC (1991): Primary 42B65, 42C15, 46B15, 41A30, 41A58
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Abstract: About fifty years ago, R. P. Boas and Harry Pollard proved that an orthonormal system that is completable by the adjunction of a finite number of functions also can be completed by multiplying the elements of the given system by a fixed, bounded, nonnegative measurable function. In subsequent years, several variations and extensions of this theorem have been given by a number of other investigators, and this program is continued here. A mildly surprising corollary of one of the results is that the trigonometric and Walsh systems can be multiplicatively transformed into quasibases for $L^{1}[0,1]$ .

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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 42B65, 42C15, 46B15, 41A30, 41A58

K. S. Kazarian
Affiliation: Departamento de Matemáticas, C-XV, Universidad Autónoma de Madrid, 28049 Madrid, Spain - Institute of Mathematics of the National Academy of Sciences, av. Marshal Bagra- mian, 24-b, 375019 Erevan, Republica Armenia
Email: kazaros.kazarian@uam.es

Robert E. Zink
Affiliation: Department of Mathematics, Purdue University, 1395 Mathematical Sciences Building, West Lafayette, Indiana 47907-1395, USA
Email: zink@math.purdue.edu

DOI: 10.1090/S0002-9947-97-02034-5
PII: S 0002-9947(97)02034-5
Keywords: Multiplicative completion, weighted $L^{p}$-spaces, Schauder basis, quasibasis, $M$-basis, approximate continuity
Received by editor(s): March 8, 1995
Received by editor(s) in revised form: July 21, 1995
Additional Notes: The first author was supported by DGICYT Spain, under Grant PB94-0149, and also by Grant MVR000 from the I.S.F
Copyright of article: Copyright 1997, American Mathematical Society

K. S. Kazarian and Robert E. Zink, Subsystems of the Schauder system that are quasibases for $L^p[0,1], 1\leq p<+\infty$, Proceedings of the AMS 126 (1998), 2883-2893. (English)

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