Nevanlinna representations in several variables

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• 作者：J. Agler^a ; R. Tully-Doyle^b ; ^{ryan.tullydoyle@hamptonu.edu" class="auth_mail" title="E-mail the corresponding author} ; N.J. Young^c ; ^d ; ^{Nicholas.Young@ncl.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：32A30 ; 30E20 ; 30E05 ; 47B25 ; 47A10
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：15 April 2016
• 年：2016
• 卷：270
• 期：8
• 页码：3000-3046
• 全文大小：597 K

文摘

We generalize to several variables the classical theorem of Nevanlinna that characterizes the Cauchy transforms of positive measures on the real line. We show that for the Loewner class, a large class of analytic functions that have non-negative imaginary part on the upper polyhalf-plane, there are representation formulae in terms of densely-defined self-adjoint operators on a Hilbert space. We find four different representation formulae and we show that every function in the Loewner class has one of the four representations, corresponding precisely to four different growth conditions at infinity.