Complete pluripolar curves and graphs

@article{TomasEdlund2004,
abstract = {It is shown that there exist $C^\{∞\}$ functions on the boundary of the unit disk whose graphs are complete pluripolar. Moreover, for any natural number k, such functions are dense in the space of $C^k$ functions on the boundary of the unit disk. We show that this result implies that the complete pluripolar closed $C^∞$ curves are dense in the space of closed $C^k$ curves in ℂⁿ. We also show that on each closed subset of the complex plane there is a continuous function whose graph is complete pluripolar.},
author = {Tomas Edlund},
journal = {Annales Polonici Mathematici},
keywords = {complete pluripolar set; lacunary series},
language = {eng},
number = {1},
pages = {75-86},
title = {Complete pluripolar curves and graphs},
url = {http://eudml.org/doc/280201},
volume = {84},
year = {2004},
}

TY - JOUR
AU - Tomas Edlund
TI - Complete pluripolar curves and graphs
JO - Annales Polonici Mathematici
PY - 2004
VL - 84
IS - 1
SP - 75
EP - 86
AB - It is shown that there exist $C^{∞}$ functions on the boundary of the unit disk whose graphs are complete pluripolar. Moreover, for any natural number k, such functions are dense in the space of $C^k$ functions on the boundary of the unit disk. We show that this result implies that the complete pluripolar closed $C^∞$ curves are dense in the space of closed $C^k$ curves in ℂⁿ. We also show that on each closed subset of the complex plane there is a continuous function whose graph is complete pluripolar.
LA - eng
KW - complete pluripolar set; lacunary series
UR - http://eudml.org/doc/280201
ER -