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Some Remarks in the Fourier Analysis
Published online by Cambridge University Press: 22 January 2016
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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
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1967
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