Commutants of the Pommiez operator
The Pommiez operator (Δf)(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 th...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1239 |
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| Summary: | The Pommiez operator (Δf)(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−λI of it. A relation between these
two types of commutants is found. |
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| ISSN: | 0161-1712 1687-0425 |