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Some Remarks in the Fourier Analysis

Published online by Cambridge University Press:  22 January 2016

Tikao Tatuzawa
Tikao Tatuzawa*
Affiliation:
Institute of Mathematics, College of General Education, University of Tokyo.
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In this paper, I should like to add some remarks to my previous note titled “Some results in the Fourier analysis” (Nagoya Math. Journal, Vol. 27, 1966). At first, we shall show that the orthnormal set exp [2 πi(m1x1+ … mnxn is complete in the Hilbert space L2 over the unit cube E = {(x1, …, xn); 0≧xj≦1 (1≦j≦n)}, where the inner product ‹f, g› for f, g ∊ L2 over E is defined by

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 29 , March 1967 , pp. 217 - 219
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967