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Operators of $ P$-variation and the evolution representation problem


Author: M. A. Freedman
Journal: Trans. Amer. Math. Soc. 279 (1983), 95-112
MSC: Primary 47D05
DOI: https://doi.org/10.1090/S0002-9947-1983-0704604-2
MathSciNet review: 704604
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Abstract: In contrast to a continuous linear semigroup, a continuous linear evolution $ U( \cdot )$ may be nondifferentiable or of unbounded variation. In order to study these evolutions we introduce a class of operator-valued functions $ A( \cdot )$ which satisfy a generalized bounded variation condition and represent $ U$ as the product integral $ U = \prod [I + dA]$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0704604-2
Keywords: $ p$-variation, evolution, product integral, Stieltjes integral
Article copyright: © Copyright 1983 American Mathematical Society

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