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The spectrum of Volterra operators on Korenblum type spaces of analytic functions

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The spectrum of Volterra operators on Korenblum type spaces of analytic functions

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Bonet Solves, JA. (2019). The spectrum of Volterra operators on Korenblum type spaces of analytic functions. Integral Equations and Operator Theory. 91(5):1-16. https://doi.org/10.1007/s00020-019-2547-x

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/157290

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Title: The spectrum of Volterra operators on Korenblum type spaces of analytic functions
Author: Bonet Solves, José Antonio
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Abstract:
[EN] The continuity, compactness and the spectrum of the Volterra integral operator V-g with symbol an analytic function g, when acting on the classical Korenblum space and other related weighted Frechet or (LB) spaces of ...[+]
Subjects: Spectrum , Integral operator , Volterra operator , Analytic functions , Growth Banach spaces , Korenblum space , Frechet spaces , (LB)-spaces
Copyrigths: Reserva de todos los derechos
Source:
Integral Equations and Operator Theory. (issn: 0378-620X )
DOI: 10.1007/s00020-019-2547-x
Publisher:
Springer-Verlag
Publisher version: https://doi.org/10.1007/s00020-019-2547-x
Project ID:
AGENCIA ESTATAL DE INVESTIGACION/MTM2016-76647-P
GENERALITAT VALENCIANA/PROMETEO/2017/102
Thanks:
This research was partially supported by the Projects MTM2016-76647-P and GV Prometeo/2017/102.
Type: Artículo

References

Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in growth Banach spaces of analytic functions. Integral Equ. Oper. Theory 86, 97–112 (2016)

Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator on Korenblum type spaces of analytic functions. Collect. Math. 69, 263–281 (2018)

Aleman, A., Constantin, O.: Spectra of integration operators on weighted Bergman spaces. J. Anal. Math. 109, 199–231 (2009) [+]
Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in growth Banach spaces of analytic functions. Integral Equ. Oper. Theory 86, 97–112 (2016)

Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator on Korenblum type spaces of analytic functions. Collect. Math. 69, 263–281 (2018)

Aleman, A., Constantin, O.: Spectra of integration operators on weighted Bergman spaces. J. Anal. Math. 109, 199–231 (2009)

Aleman, A., Peláez, J.A.: Spectra of integration operators and weighted square functions. Indiana Univ. Math. J. 61, 1–19 (2012)

Aleman, A., Persson, A.-M.: Resolvent estimates and decomposable extensions of generalized Cesàro operators. J. Funct. Anal. 258, 67–98 (2010)

Aleman, A., Siskakis, A.G.: An integral operator on $$H^p$$. Complex Var. Theory Appl. 28, 149–158 (1995)

Aleman, A., Siskakis, A.G.: Integration operators on Bergman spaces. Indiana Univ. Math. J. 46, 337–356 (1997)

Basallote, M., Contreras, M.D., Hernández-Mancera, C., Martín, M.J., Paúl, P.J.: Volterra operators and semigroups in weighted Banach spaces of analytic functions. Collect. Math. 65, 233–249 (2014)

Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Stud. Math. 127, 137–168 (1998)

Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Austral. Math. Soc. Ser. A 54(1), 70–79 (1993)

Blasco, O., Girela, D., Márquez, M.A.: Mean growth of the derivative of analytic functions, bounded mean oscillation and normal functions. Indiana Univ. Math. J. 47, 893–912 (1998)

Bonet, J.: The spectrum of Volterra operators on weighted spaces of entire functions. Q. J. Math. 66, 799–807 (2015)

Constantin, O.: A Volterra-type integration operator on Fock spaces. Proc. Am. Math. Soc. 140, 4247–4257 (2012)

Constantin, O., Persson, A.-M.: The spectrum of Volterra-type integration operators on generalized Fock spaces. Bull. London Math. Soc. 47, 958–963 (2015)

Contreras, M., Hernández-Díaz, A.G.: Weighted composition operators in weighted Banach spacs of analytic functions. J. Austral. Math. Soc. (Ser. A) 69, 41–60 (2000)

Duren, P.: Theory of $$H^p$$ Spaces. Academic Press, New York (1970)

Girela, D., González, C., Peláez, J.A.: Multiplication and division by inner functions in the space of Bloch functions. Proc. Am. Math. Soc. 134, 1309–1314 (2006)

Harutyunyan, A., Lusky, W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Stud. Math. 184, 233–247 (2008)

Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Grad. Texts in Math. 199, Springer, New York (2000)

Hu, Z.: Extended Cesàro operators on mixed-norm spaces. Proc. Am. Math. Soc. 131, 2171–2179 (2003)

Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)

Korenblum, B.: An extension of the Nevanlinna theory. Acta Math. 135, 187–219 (1975)

Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomophic functions. Stud. Math. 75, 19–45 (2006)

Malman, B.: Spectra of generalized Cesáro operators acting on growth spaces. Integr. Equ. Oper. Theory 90, 26 (2018)

Meise, R., Vogt, D.: Introduction to Functional Analysis, Vol 2 of Oxford Graduate Texts in Mathematics. The Clarendon Press, New York (1997)

Persson, A.-M.: On the spectrum of the Cesàro operator on spaces of analytic functions. J. Math. Anal. Appl. 340, 1180–1203 (2008)

Pommerenke, C.: Schlichte Funktionen un analytische Functionen von beschrn̈kter mittlerer Oszilation. Comment. Math. Helv. 52, 591–602 (1977)

Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287–302 (1971)

Siskakis, A.: Volterra operators on spaces of analytic functions–a survey. In: Proceedings of the First Advanced Course in Operator Theory and Complex Analysis, Univ. Sevilla Serc. Publ., Seville, 2006, pp. 51–68 (2006)

Stević, S.: Boundedness and compactness of an integral operator on a weighted space on the polydisc. Indian J. Pure Appl. Math. 37, 343–355 (2006)

Vasilescu, F.H.: Analytic functional calculus and spectral decompositions. Translated from the Romanian. Mathematics and its Applications (East European Series), 1. D. Reidel Publishing Co., Dordrecht (1982)

Zhu, K.: Operator Theory on Function Spaces, Math. Surveys and Monographs Vo. 138. Amer. Math. Soc. (2007)

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