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UNIFORM EXTENSIONS AND SPECTRAL SYNTHESIS

MASAKITI KINUKAWA
Chinese Journal of Mathematics
Vol. 21, No. 3 (SEPTEMBER 1993), pp. 235-244
Stable URL: http://www.jstor.org/stable/43836520
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
UNIFORM EXTENSIONS AND SPECTRAL SYNTHESIS
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Abstract

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.

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