TY - JOUR
T1 - Perturbing PLA
AU - Kozma, Gady
AU - Olevskii, Alexander
N1 - Funding Information:
1Both authors partially supported by their respective Israel Science Foundation grants.
PY - 2013/10
Y1 - 2013/10
N2 - We proved earlier that every measurable function on the circle, after a uniformly small perturbation, can be written as a power series (i.e., a series of exponentials with positive frequencies), which converges almost everywhere. Here, we show that this result is basically sharp: the perturbation cannot be made smooth or even Hölder. We also discuss a similar problem for perturbations with lacunary spectrum.
AB - We proved earlier that every measurable function on the circle, after a uniformly small perturbation, can be written as a power series (i.e., a series of exponentials with positive frequencies), which converges almost everywhere. Here, we show that this result is basically sharp: the perturbation cannot be made smooth or even Hölder. We also discuss a similar problem for perturbations with lacunary spectrum.
UR - http://www.scopus.com/inward/record.url?scp=84888046826&partnerID=8YFLogxK
U2 - 10.1007/s11854-013-0036-8
DO - 10.1007/s11854-013-0036-8
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AN - SCOPUS:84888046826
SN - 0021-7670
VL - 121
SP - 279
EP - 298
JO - Journal d'Analyse Mathematique
JF - Journal d'Analyse Mathematique
IS - 1
ER -