Multiple Shift Operator with Simple Spectrum

  • N. K. Nikol’skii
Part of the Seminars in Mathematics book series (SM)


In this note we consider the spectrum multiplicity and operator cyclicity problems for operators of the form U × U × ... × U, where U is the (bilateral) shift operator in a certain sequence space X. Necessary and sufficient conditions for simplicity of the spectrum are obtained which are close to one another and coincide in many important spaces (lp, Orlicz, etc.). These hypotheses are closely allied with the possible realization of X by measurable functions and functions having singular measures with limiting rate of decrease of the Fourier coefficients.


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© Springer Science+Business Media New York 1972

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  • N. K. Nikol’skii

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