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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| Format: | Article |
| Language: | English |
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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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| author | Ivan H. Dimovski Valentin Z. Hristov |
| author_facet | Ivan H. Dimovski Valentin Z. Hristov |
| author_sort | Ivan H. Dimovski |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-96a07f7ba54a49209e33d4f135dea10e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-96a07f7ba54a49209e33d4f135dea10e2025-02-03T00:59:31ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-01200581239125110.1155/IJMMS.2005.1239Commutants of the Pommiez operatorIvan H. Dimovski0Valentin Z. Hristov1Department of Complex Analysis, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street Block 8, Sofia 1113, BulgariaDepartment of Complex Analysis, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street Block 8, Sofia 1113, BulgariaThe 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.http://dx.doi.org/10.1155/IJMMS.2005.1239 |
| spellingShingle | Ivan H. Dimovski Valentin Z. Hristov Commutants of the Pommiez operator International Journal of Mathematics and Mathematical Sciences |
| title | Commutants of the Pommiez operator |
| title_full | Commutants of the Pommiez operator |
| title_fullStr | Commutants of the Pommiez operator |
| title_full_unstemmed | Commutants of the Pommiez operator |
| title_short | Commutants of the Pommiez operator |
| title_sort | commutants of the pommiez operator |
| url | http://dx.doi.org/10.1155/IJMMS.2005.1239 |
| work_keys_str_mv | AT ivanhdimovski commutantsofthepommiezoperator AT valentinzhristov commutantsofthepommiezoperator |