Königs eigenfunction for composition operators on Bloch and H<sup>∞sup> type spaces

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• 作者：Ted Eklund<sup>asup><sup> ; sup><sup>ted.eklund@abo.fi" class="auth_mail" title="E-mail the corresponding authorsup> ; Pablo Galindo<sup>bsup><sup> ; sup><sup>1sup><sup> ; sup><sup>pablo.galindo@uv.es" class="auth_mail" title="E-mail the corresponding authorsup> ; Mikael Lindstr&ouml ; m<sup>asup><sup> ; sup><sup>mikael.lindstrom@abo.fi" class="auth_mail" title="E-mail the corresponding authorsup>
• 关键词：Composition operator ; K&ouml ; nigs eigenfunction
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：445
• 期：2
• 页码：1300-1309
• 全文大小：328 K

文摘

We discuss when the K&ouml;nigs eigenfunction associated with a non-automorphic selfmap of the complex unit disc that fixes the origin belongs to Banach spaces of holomorphic functions of Bloch and <span id="mmlsi1" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300816&_mathId=si1.gif&_user=111111111&_pii=S0022247X16300816&_rdoc=1&_issn=0022247X&md5=9c822e7f1a28ff630fcabca84649b443" title="Click to view the MathML source">H<sup>∞sup>span><span class="mathContainer hidden"><span class="mathCode">scroll">sup>H∞sup>span>span>span> type. In the latter case, our characterization answers a question of P. Bourdon. Some spectral properties of composition operators on <span id="mmlsi1" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16300816&_mathId=si1.gif&_user=111111111&_pii=S0022247X16300816&_rdoc=1&_issn=0022247X&md5=9c822e7f1a28ff630fcabca84649b443" title="Click to view the MathML source">H<sup>∞sup>span><span class="mathContainer hidden"><span class="mathCode">scroll">sup>H∞sup>span>span>span> for unbounded K&ouml;nigs eigenfunction are obtained.