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The subnormal completion problem on a directed tree is to de-termine, given a collection of weights on a subtree, whether the weightsmay be completed to the weights of a subnormal weighted shift on thedirected tree. We study this problem on a directed tree with a singlebranching point,ηbranches and the trunk of length 1 and its subtreewhich is the “truncation” of the full tree to vertices of generation notexceeding 2. We provide necessary and sufficient conditions written interms of two parameter sequences for the existence of a subnormal com-pletion in which the resulting measures are 2-atomic. As a consequence,we obtain a solution of the subnormal completion problem for this pairof directed trees whenη<∞.Ifη= 2, we present a solution writtenexplicitly in terms of initial data.
słowa kluczowe w j. angielskim:
subnormal operator, weighted shift on a directed tree, subnormal completion problem, 2-atomic measures
liczba arkuszy wydawniczych:
1,3
wydział: instytut / zakład / katedra:
Wydział Matematyki i Informatyki : Instytut Matematyki