Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A class of complete orthogonal sequences of step functions


Authors: J. L. Sox and W. J. Harrington
Journal: Trans. Amer. Math. Soc. 157 (1971), 129-135
MSC: Primary 42.15
DOI: https://doi.org/10.1090/S0002-9947-1971-0275046-3
MathSciNet review: 0275046
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A class of orthogonal sets of step functions is defined and each member is shown to be complete in $ {L_2}(0,1)$. Pointwise convergence theorems are obtained for the Fourier expansions relative to these sets. The classical Haar orthogonal set is shown to be a set of this class and the class itself is seen to be a subclass of the ``generalized Haar systems'' defined recently by Price.


References [Enhancements On Off] (What's this?)

  • [1] P. Franklin, A set of continuous orthogonal functions, Math. Ann. 100 (1928), 522-529. MR 1512499
  • [2] A. Haar, Zur Theorie der Orthogonalen Funktionenysystems, Math. Ann. 69 (1910), 331-371. MR 1511592
  • [3] J. J. Price, An algebraic characterization of certain orthonormal systems, Proc. Amer. Math. Soc. 19 (1968), 268-273. MR 37 #682. MR 0225085 (37:682)
  • [4] A. Zygmund, Trigonometrical series, 2nd rev. ed., Cambridge Univ. Press, New York, 1959. MR 21 #6498. MR 0107776 (21:6498)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42.15

Retrieve articles in all journals with MSC: 42.15


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0275046-3
Keywords: Haar functions, Fourier analysis, orthonormal set of functions, complete in $ {L_2}(0,1)$, pointwise convergence, generalized Haar system
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society