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UNIFORM EXTENSIONS AND SPECTRAL SYNTHESIS
Chinese Journal of Mathematics
Vol. 21, No. 3 (SEPTEMBER 1993), pp. 235-244
Published by: Mathematical Society of the Republic of China
Stable URL: http://www.jstor.org/stable/43836520
Page Count: 10
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In 1979, Wan-Chen Hsieh proved that a topology T on L∞ (R) is synthesizable if and only if each function f(x) of the dual space (L∞(R), T)′ has a uniformly extendible Fourier transform. In his proof he used a result of spectral analysis of bounded functions due to A. Beurling. Beurling's argument depends on the one dimensional property and his method seems to be ineffective to extend the result to the general dimension spaces. In this paper we give the general k dimensional analogue of Hsieh's result and the contraction theorem. We give also a general form of the Bernstein theorem.
Chinese Journal of Mathematics © 1993 Mathematical Society of the Republic of China