Abstract:
Motivated by the Invariant Subspace Problem, we describe explicitly the closed subspace H 2 generated by the limit points in the H 2 norm of the orbit of a thin Blaschke product B under composition operators C φ induced by non-elliptic automorphisms. This description exhibits a surprising connection to model spaces. Finally, we give a constructive characterization of the C φ-eigenfunctions in H p for 1≤p≤∞. © 2011 Elsevier Inc.
Registro:
| Documento: |
Artículo
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| Título: | Orbits of non-elliptic disc automorphisms on H p |
| Autor: | Gallardo-Gutiérrez, E.A.; Gorkin, P.; Suárez, D. |
| Filiación: | Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid e IUMA, Plaza de Ciencias 3, 28040 Madrid, Spain
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, United States
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, (1428) Nuñez, Cap. Fed., Argentina
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| Palabras clave: | Blaschke products; Eigenfunctions of composition operators; Invariant subspaces |
| Año: | 2012
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| Volumen: | 388
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| Número: | 2
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| Página de inicio: | 1013
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| Página de fin: | 1026
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| DOI: |
http://dx.doi.org/10.1016/j.jmaa.2011.10.048 |
| Título revista: | Journal of Mathematical Analysis and Applications
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| Título revista abreviado: | J. Math. Anal. Appl.
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| ISSN: | 0022247X
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| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0022247X_v388_n2_p1013_GallardoGutierrez.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v388_n2_p1013_GallardoGutierrez |
Referencias:
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- Nordgren, E.A., Rosenthal, P., Wintrobe, F.S., Composition operators and the invariant subspace problem (1984) C. R. Mat. Rep. Acad. Sci. Can., 6, pp. 279-282
- Nordgren, E.A., Rosenthal, P., Wintrobe, F.S., Invertible composition operators on H p (1987) J. Funct. Anal., 73, pp. 324-344
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Citas:
---------- APA ----------
Gallardo-Gutiérrez, E.A., Gorkin, P. & Suárez, D.
(2012)
. Orbits of non-elliptic disc automorphisms on H p. Journal of Mathematical Analysis and Applications, 388(2), 1013-1026.
http://dx.doi.org/10.1016/j.jmaa.2011.10.048---------- CHICAGO ----------
Gallardo-Gutiérrez, E.A., Gorkin, P., Suárez, D.
"Orbits of non-elliptic disc automorphisms on H p"
. Journal of Mathematical Analysis and Applications 388, no. 2
(2012) : 1013-1026.
http://dx.doi.org/10.1016/j.jmaa.2011.10.048---------- MLA ----------
Gallardo-Gutiérrez, E.A., Gorkin, P., Suárez, D.
"Orbits of non-elliptic disc automorphisms on H p"
. Journal of Mathematical Analysis and Applications, vol. 388, no. 2, 2012, pp. 1013-1026.
http://dx.doi.org/10.1016/j.jmaa.2011.10.048---------- VANCOUVER ----------
Gallardo-Gutiérrez, E.A., Gorkin, P., Suárez, D. Orbits of non-elliptic disc automorphisms on H p. J. Math. Anal. Appl. 2012;388(2):1013-1026.
http://dx.doi.org/10.1016/j.jmaa.2011.10.048