Abstract
Let be any of the spaces , , , and , and let , . A number of necessary conditions and sufficient conditions for the ‘perturbed trigonometric system’ , , to be equivalent to the trigonometric system , , in the space for any are obtained. In particular, it is shown that if , where , then this equivalence takes place, the exponent being sharp. This result is used to show that in , , there exist bases of exponentials which are not equivalent to the trigonometric basis. The machinery of Fourier multipliers is used in the proofs. Bibliography: 18 titles.
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