Commutants of the Pommiez operator

Ivan H. Dimovski and Valentin Z. Hristov

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-13

Abstract:

The Pommiez operator ( Δ f ) ( z ) = ( f ( z ) − f ( 0 ) ) / z is considered in the space ℋ ( G ) of the holomorphic functions in an arbitrary finite Runge domain G . A new proof of a representation formula of Linchuk of the commutant of Δ in ℋ ( G ) is given. The main result is a representation formula of the commutant of the Pommiez operator in an arbitrary invariant hyperplane of ℋ ( G ) . It uses an explicit convolution product for an arbitrary right inverse operator of Δ or of a perturbation Δ − λ I of it. A relation between these two types of commutants is found.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:584354

DOI: 10.1155/IJMMS.2005.1239

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