Abstract
In this paper we prove the existence of nonzero measures of the sort mentioned in the title. In particular, we prove that any set whose closure contains interior points supports such a measure.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 73, pp. 7–15, 1977.
The author thanks N. K. Nikol'skii for his interest in the work and S. V. Khrushchev for help in formulating it.
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Aleksandrov, A.B. Discrete measures with compact nowhere dense support, orthogonal to rational functions. J Math Sci 34, 2023–2028 (1986). https://doi.org/10.1007/BF01741575
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DOI: https://doi.org/10.1007/BF01741575