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Disintegration‐of‐measure techniques for commuting multivariable weighted shifts
Author(s) -
Curto Raúl E.,
Yoon Jasang
Publication year - 2006
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611505015601
Subject(s) - mathematics , measure (data warehouse) , tuple , multivariable calculus , variable (mathematics) , row , weighted arithmetic mean , combinatorics , statistics , discrete mathematics , mathematical analysis , data mining , computer science , control engineering , database , engineering
We employ techniques from the theory of disintegration of measures to study the Lifting Problem for commuting n ‐tuples of subnormal weighted shifts. We obtain a new necessary condition for the existence of a lifting, and generate new pathology associated with bringing together the Berger measures associated to each individual weighted shift. For subnormal 2‐variable weighted shifts, we then find the precise relation between the Berger measure of the pair and the Berger measures of the shifts associated to horizontal rows and vertical columns of weights. 2000 Mathematics Subject Classification 47B20, 47B37, 47A13, 28A50 (primary), 44A60, 47‐04, 47A20 (secondary).