Journal article
Solution of the reconstruction-of-the-measure problem for canonical invariant subspaces
Annali di matematica pura ed applicata, Vol.201, pp.1489-1504
10/05/2021
DOI: 10.1007/s10231-021-01166-7
Abstract
We study the Reconstruction-of-the-Measure Problem (ROMP) for commuting 2-variable weighted shifts W-(alpha,W-beta), when the initial data are given as the Berger measure of the restriction of W-(alpha,W-beta) to a canonical invariant subspace, together with the marginal measures for the 0-th row and 0-th column in the weight diagram for W-(alpha,W-beta). We prove that the natural necessary conditions are indeed sufficient. When the initial data correspond to a soluble problem, we give a concrete formula for the Berger measure of W-(alpha,W-beta). Our strategy is to build on previous results for back-step extensions and one-step extensions. A key new theorem allows us to solve ROMP for two-step extensions. This, in turn, leads to a solution of ROMP for arbitrary canonical invariant subspaces of l(2) (Z(+)(2)).
Details
- Title: Subtitle
- Solution of the reconstruction-of-the-measure problem for canonical invariant subspaces
- Creators
- Raul E Curto - University of IowaSang Hoon Lee - Chungnam National UniversityJasang Yoon - The University of Texas Rio Grande Valley
- Resource Type
- Journal article
- Publication Details
- Annali di matematica pura ed applicata, Vol.201, pp.1489-1504
- DOI
- 10.1007/s10231-021-01166-7
- ISSN
- 0373-3114
- eISSN
- 1618-1891
- Publisher
- SPRINGER HEIDELBERG
- Number of pages
- 16
- Grant note
- University of Texas System Consejo Nacional de Ciencia y Tecnologia de Mexico (CONACYT); Consejo Nacional de Ciencia y Tecnologia (CONACyT) 2020R1A2C1A0100584611 / NRF (Korea)
- Language
- English
- Date published
- 10/05/2021
- Academic Unit
- Mathematics
- Record Identifier
- 9984240871902771
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