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| A Connection Between the Logarithmic Capacity and the Sequence of theAnalytical Function |
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Citation： |
Mo Guoduan.A Connection Between the Logarithmic Capacity and the Sequence of theAnalytical Function[J].Chinese Annals of Mathematics B,1982,3(2):189~194 |
| Page view： 878
Net amount： 702 |
Authors： |
Mo Guoduan; |
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| Abstract： |
Let E be a bounded closed set, d(E) be the logarithmic capacity of E. If A is any bounded set, then
$[d(A) = \mathop {\sup }\limits_{E \in A} d(E)\]$
For each $Z_0 \in E$, and $\delta >0$, let
$[\Delta = \Delta _{{Z_0}}^\delta = CE \cap (|Z - {Z_0}| < \delta )\]$
where CE is complement of E, then \Delta is an open set. By [{\bar \Delta ^0}\] we denote the interior of the closure A of A. Clearly,$\Delta \subset [{\bar \Delta ^0}\]$ and $d(\Delta) \leq d([{\bar \Delta ^0}\])$,
and there exists an open set D such that d(D) 0, the equation
$d(\Delta)=d([{\bar \Delta ^0}\])$ holds. |
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