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Title: | Values of sequences of purely periodic functions |
Authors: | Dangskul S. Laohakosol V. Tangsupphathawat P. |
Issue Date: | 2012 |
Abstract: | Let f: ℝ → ℝ be a nonzero purely periodic function with least period P. For θ (≠ 0) and b both in the interval [0; P), it is shown that when n runs through the nonnegative integers, the nonzero sequence (f(nθ + b)) is purely periodic if θ is a rational multiple of P. While if θ is not a rational multiple of P and f is continuous, the sequence (f(nθ + b)) is dense in the range of f. Moreover, under appropriate conditions, a sequence of the form (∑ d r=1α rf (Pns r/t r + b r)) with rationals s r/t r is shown to be purely periodic with least period being the least common multiple of t 1,...,t d. |
URI: | https://ir.swu.ac.th/jspui/handle/123456789/14352 https://www.scopus.com/inward/record.uri?eid=2-s2.0-84859447663&partnerID=40&md5=3994b1f18cbc8364d7cc3ac6093ec5eb |
ISSN: | 16072510 |
Appears in Collections: | Scopus 1983-2021 |
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