Nevanlinna counting function and pull–back measure
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- by O. El-Fallah and K. Kellay
- Proc. Amer. Math. Soc. 144 (2016), 2559-2564
- DOI: https://doi.org/10.1090/proc/12913
- Published electronically: October 21, 2015
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Abstract:
We give an explicit relation between the Nevanlinna counting function of an analytic self-map of the unit disk and its pull-back measure. This gives a simple proof of the results of Lefévre, Li, Queffélec and Rodrìguez–Piazza (2011).References
- Christopher J. Bishop, Orthogonal functions in $H^\infty$, Pacific J. Math. 220 (2005), no. 1, 1–31. MR 2195060, DOI 10.2140/pjm.2005.220.1
- E. Essén, D. F. Shea, and C. S. Stanton, A value–distribution criterion for the class $L\log L$ and some related questions, Ann. Inst. Fourier (Grenoble), 35 (1985) 125–150.
- Pascal Lefèvre, Daniel Li, Hervé Queffélec, and Luis Rodríguez-Piazza, Nevanlinna counting function and Carleson function of analytic maps, Math. Ann. 351 (2011), no. 2, 305–326. MR 2836660, DOI 10.1007/s00208-010-0596-1
- Pascal Lefèvre, Daniel Li, Hervé Queffélec, and Luis Rodríguez-Piazza, Some examples of compact composition operators on $H^2$, J. Funct. Anal. 255 (2008), no. 11, 3098–3124. MR 2464571, DOI 10.1016/j.jfa.2008.06.027
- Barbara D. MacCluer, Compact composition operators on $H^p(B_N)$, Michigan Math. J. 32 (1985), no. 2, 237–248. MR 783578, DOI 10.1307/mmj/1029003191
- Walter Rudin, A generalization of a theorem of Frostman, Math. Scand. 21 (1967), 136–143 (1968). MR 235151, DOI 10.7146/math.scand.a-10853
- Joel H. Shapiro, Composition operators and classical function theory, Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993. MR 1237406, DOI 10.1007/978-1-4612-0887-7
- Joel H. Shapiro, The essential norm of a composition operator, Ann. of Math. (2) 125 (1987), no. 2, 375–404. MR 881273, DOI 10.2307/1971314
Bibliographic Information
- O. El-Fallah
- Affiliation: Laboratoire Analyse et Applications URAC/03, Université Mohammed V–Rabat, B.P. 1014 Rabat, Morocco
- MR Author ID: 338521
- Email: elfallah@fsr.ac.ma
- K. Kellay
- Affiliation: Institut de Mathématiques de Bordeaux, Université de Bordeaux, 351 cours de la Liberation, 33405 Talence, France
- Email: kkellay@math.u-bordeaux1.fr
- Received by editor(s): April 8, 2015
- Received by editor(s) in revised form: July 20, 2015
- Published electronically: October 21, 2015
- Additional Notes: The first author was supported by CNRST (URAC/03) and Académie Hassan II des sciences et techniques
- Communicated by: Pamela B. Gorkin
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2559-2564
- MSC (2010): Primary 30C80, 47B33, 47B10, 47A15
- DOI: https://doi.org/10.1090/proc/12913
- MathSciNet review: 3477072