Capacity Estimates for Planar Cantor-Like Sets
Keyword(s):
Upper and lower bounds for the capacity of planar Cantor-like sets are presented. Chebichev polynomials are the principal tool employed in the derivation of these estimates. A necessary and sufficient condition for certain planar Cantor-like sets to have positive capacity is obtained. Related one-sided capacitary estimates for more general Cantor-like sets can be found in [3, pp. 106-109]. Techniques analogous to those used in this paper yield similar results for linear Cantor-like sets which are well-known [2, pp. 150-161]. The use of Chebichev polynomials to obtain these results provides an alternate, possibly more elementary, approach to these linear problems.
1971 ◽
Vol 3
(01)
◽
pp. 120-154
◽
2021 ◽
1989 ◽
Vol 32
(1)
◽
pp. 121-126
◽
2018 ◽
Vol 50
(2)
◽
pp. 187-198
◽
1994 ◽
Vol 124
(4)
◽
pp. 811-823
2017 ◽
Vol E100.A
(12)
◽
pp. 2764-2775
◽