A new approach to the 2-variable Subnormal Completion Problem |
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Authors: | Raúl E Curto Sang Hoon Lee Jasang Yoon |
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Institution: | a Department of Mathematics, The University of Iowa, Iowa City, IA 52242, United States b Department of Mathematics, Chungnam National University, Daejeon, 305-764, Republic of Korea c Department of Mathematics, The University of Texas-Pan American, Edinburg, TX 78539, United States |
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Abstract: | We study the Subnormal Completion Problem (SCP) for 2-variable weighted shifts. We use tools and techniques from the theory of truncated moment problems to give a general strategy to solve SCP. We then show that when all quadratic moments are known (equivalently, when the initial segment of weights consists of five independent data points), the natural necessary conditions for the existence of a subnormal completion are also sufficient. To calculate explicitly the associated Berger measure, we compute the algebraic variety of the associated truncated moment problem; it turns out that this algebraic variety is precisely the support of the Berger measure of the subnormal completion. |
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Keywords: | Subnormal Completion Problem Subnormal pair 2-Variable weighted shift Moment problems k-Hyponormal pairs |
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