Journal article
DUAL PAIRS OF OPERATORS, HARMONIC ANALYSIS OF SINGULAR NONATOMIC MEASURES AND KREIN-FELLER DIFFUSION
Journal of operator theory, Vol.89(1), pp.205-248
01/01/2023
DOI: 10.7900/jot.2021may30.2359
Abstract
We show that a Krein-Feller operator is naturally associated to a fixed measure 14, (positive, cr-finite, and nonatomic). Dual pairs of operators are introduced, carried by the two Hilbert spaces, L2(14) and L2(A), where A denotes Lebesgue measure. An associated operator pair consists of two densely defined operators, each one contained in the adjoint of the other. This yields a rigorous analysis of the corresponding 14-Krein-Feller operator. As an application, including the case of fractal measures, we compute the associated diffusion, semigroup, Dirichlet forms, and 14-generalized heat equation.
Details
- Title: Subtitle
- DUAL PAIRS OF OPERATORS, HARMONIC ANALYSIS OF SINGULAR NONATOMIC MEASURES AND KREIN-FELLER DIFFUSION
- Creators
- Palle E. T. Jorgensen - Univ Iowa, Dept Math, Iowa City, IA 52242 USAJames Tian - Math Reviews, 416 4th St, Ann Arbor, MI 48103 USA
- Resource Type
- Journal article
- Publication Details
- Journal of operator theory, Vol.89(1), pp.205-248
- Publisher
- Theta Foundation
- DOI
- 10.7900/jot.2021may30.2359
- ISSN
- 0379-4024
- eISSN
- 1841-7744
- Number of pages
- 44
- Language
- English
- Date published
- 01/01/2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984386253902771
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