Haar and Walsh Fourier Series of Perron Integrable Functions

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Authors

  • William R. Wade
     University of Tennessee ,US

Abstract

Denote the Walsh functions by φ0, φ1, φ2...... and the Haar functions by χ0, χ1, χ2, ...... Definitions of both complete orthonormal systems may be found in [1], [2], or [5].

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Published

1974-12-01

How to Cite

Wade, W. R. (1974). Haar and Walsh Fourier Series of Perron Integrable Functions. The Journal of the Indian Mathematical Society, 38(1-4), 19–35. Retrieved from https://informaticsjournals.com/index.php/jims/article/view/16678

Issue

Volume 38, Issue 1-4, March-December 1974

Section

Articles

License

Copyright (c) 1974 William R. Wade

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

G. ALEXITS : Converge/ice Problems of Orthogonal Functions, transl. by I. Foldes, Pergamon Press, New York, 1961.

F. G. ARUTUNJAN : On the Recovery of coefficients of Haar and Walsh Series which converge to a Denjoy Integrable Function, hv. Akad. Nauk S. S. S. R. 30(1966, 325-344 (Russian).

S. SAKS : Theory of the Integral, Hafner, New York, 1937.

V. A. SKVORCOV : On Haar Series with Convergent Subsequences of Partial Sums, Dokl. Akad. Nauk S. S. S. R. (4) 183 (1968), translated as Soviet Math. Dokl. Vol. 9. (1968), No. 6, 1469-1471.

W. R. WADE : A Uniqueness Theorem for Haar and Walsh Series, Trans. A.M. S. 141 (1969), 187-194.

W. R. WADE : M-Sets for Haar and Walsh Series, to appear.

A. ZYGMUND : Trigonometric Series, Vol. II, Cambridge University Press, Cambridge, 1959.