Abstract
Functions whose translates span L p(R) are called L p-cyclic functions. For a fixed p \memb [1, \infty], we construct Schwartz-class functions which are L r -cyclic for r > p and not L r- cyclic for r \le p. We then construct Schwartz-class functions which are L r -cyclic for r \ge p and not L r -cyclic for r < p. The constructions differ for p \memb (1, 2) and p > 2.
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Communicated by John J. Benedetto.
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Rosenblatt, J., Shuman, K. Cyclic Functions in L p(R), 1 \le p < \infty. J. Fourier Anal. Appl. 9, 289–300 (2003). https://doi.org/10.1007/s00041-003-0015-z
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DOI: https://doi.org/10.1007/s00041-003-0015-z