Haar and Walsh Fourier Series of Perron Integrable Functions
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].Downloads
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Copyright (c) 1974 William R. Wade
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.
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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.