<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MARK ELIN</style></author><author><style face="normal" font="default" size="100%">MARINA LEVENSHTEIN</style></author><author><style face="normal" font="default" size="100%">DAVID SHOIKHET</style></author><author><style face="normal" font="default" size="100%">ROBERTO TAURASO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">RIGIDITY OF HOLOMORPHIC GENERATORS AND ONE-PARAMETER SEMIGROUPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">30D05</style></keyword><keyword><style  face="normal" font="default" size="100%">32H12</style></keyword><keyword><style  face="normal" font="default" size="100%">47B33</style></keyword><keyword><style  face="normal" font="default" size="100%">47H20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/251-266-DSA-26-08-Elin.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we establish a rigidity property of holomorphic generators by using their local behavior at a boundary point τ of the open unit disk ∆. Namely,&amp;nbsp; if f ∈ Hol(∆, C) is the generator of a&amp;nbsp; one- parameter continuous semigroup&amp;nbsp; {F&lt;sub&gt;t&lt;/sub&gt; }&lt;sub&gt;t&amp;nbsp;&lt;/sub&gt;≥ 0, we show that the equality f(z) = o (|z − τ |&lt;sup&gt;3&lt;/sup&gt;)&amp;nbsp;when z → τ in each non-tangential approach region at τ implies that f vanishes identically on ∆. Note, that if F is a self-mapping of ∆ then f = I − F is a generator, so our result extends the boundary version of the Schwarz Lemma obtained by D. Burns and S. Krantz. We also prove that two semigroups &amp;nbsp;{ F&lt;sub&gt;t&lt;/sub&gt; }&lt;sub&gt;t&amp;nbsp;&lt;/sub&gt;≥ 0 and { G&lt;sub&gt;t&lt;/sub&gt; }&lt;sub&gt;t&amp;nbsp;&lt;/sub&gt;≥ 0, with generators f and g respectively, commute if and only if the equality f = αg holds for some complex constant α. This fact gives simple conditions on the generators of two commuting semigroups at their common null point τ under which the semigroups coincide identically on ∆.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">251</style></section></record></records></xml>