Geodesic
On Some Properties and Examples of Nevanlinna Domains
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 204-213.

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The properties of Nevanlinna domains are considered. These domains arise in the problems of approximation by polyanalytic functions. Several analytic and geometric properties (both new and earlier known) of Nevanlinna domains are described. In particular, a new method for constructing Nevanlinna domains with boundaries belonging to the class $\mathrm C^1$ is proposed, and new examples of such domains whose boundaries do not belong to the class $\mathrm C^{1,\alpha }$ for $\alpha \in (0,1)$ are presented. This method is based on the property of pseudocontinuation of a conformal mapping from the unit disk onto a Nevanlinna domain. 
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K. Yu. Fedorovskiy. On Some Properties and Examples of Nevanlinna Domains. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 204-213. http://geodesic.mathdoc.fr/item/TM_2006_253_a14/

[1] Karmona Kh.Kh., Paramonov P.V., Fedorovskii K.Yu., “O ravnomernoi approksimatsii polianaliticheskimi mnogochlenami i zadache Dirikhle dlya bianaliticheskikh funktsii”, Mat. sb., 193:10 (2002), 75–98 | MR

[2] Privalov I.I., Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M.; L., 1950

[3] Fedorovskii K.Yu., “O ravnomernykh priblizheniyakh funktsii $n$-analiticheskimi polinomami na spryamlyaemykh konturakh v $\mathbb C$”, Mat. zametki, 59:4 (1996), 604–610 | MR | Zbl

[4] Buave A., Gote P.M., Paramonov P.V., “O ravnomernoi approksimatsii $n$-analiticheskimi funktsiyami na zamknutykh mnozhestvakh v $\mathbb C$”, Izv. RAN. Ser. mat., 68:3 (2004), 15–28 | MR

[5] Boven A., Paramonov P.V., “Approksimatsiya meromorfnymi i tselymi resheniyami ellipticheskikh uravnenii v banakhovykh prostranstvakh raspredelenii”, Mat. sb., 189:4 (1998), 3–24 | MR

[6] Carmona J.J., Fedorovskiy K.Yu., “Conformal maps and uniform approximation by polyanalytic functions”, Selected topics in complex analysis, Oper. Theory. Adv. and Appl., 158, Birkhäuser, Basel, 2005, 109–130 | MR | Zbl

[7] Fedorovskii K.Yu., “Approksimatsiya i granichnye svoistva polianaliticheskikh funktsii”, Tr. MIAN, 235, 2001, 262–271 | MR | Zbl

[8] Mazalov M.Ya., “Primer nepostoyannoi bianaliticheskoi funktsii, obraschayuscheisya v nul vsyudu na nigde ne analiticheskoi granitse”, Mat. zametki, 62:4 (1997), 629–632 | MR | Zbl

[9] Shapiro H.S., “Generalized analytic continuation”, Symp. Theor. Phys. and Math., 8 (1968), 151–163 | MR | Zbl

[10] Douglas R.G., Shapiro H.S., Shields A.L., “Cyclic vectors and invariant subspaces of the backward shift operator”, Ann. Inst. Fourier, 20:1 (1970), 37–76 | MR | Zbl

[11] Davis P., The Schwarz function and its applications, Carus Math. Monogr., 17, Math. Assoc. Amer., Buffalo (NY), 1974 | MR | Zbl

[12] Gofman K., Banakhovy prostranstva analiticheskikh funktsii, Izd-vo inostr. lit., M., 1963

[13] Putinar M., Shapiro H.S., “The Friedrichs operator of a planar domain”, Complex analysis, operators, and related topics, Oper. Theory. Adv. and Appl., 113, Birkhäuser, Basel, 2000, 303–330 | MR | Zbl

[14] Ahern P.R., Clark D.N., “On functions orthogonal to invariant subspaces”, Acta math., 124 (1970), 191–204 | DOI | MR | Zbl

[15] Pommerenke Ch., Boundary behavior of conformal maps, Springer, Berlin, 1992 | MR | Zbl