Geodesic
Analytic Wavelets in Multiply Connected Domains with Circular Boundaries
Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 400-416.

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Wavelet bases in Hardy-type spaces of analytic functions in a domain with circular boundaries are constructed from a wavelet basis in the Hardy space of functions analytic in the disk. An estimate of the rate of convergence of the partial sums of the constructed wavelets is also obtained.
Keywords: analytic wavelet, basis in a Hardy-type space of analytic functions, wavelet expansion. 
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G. A. Dubosarskij. Analytic Wavelets in Multiply Connected Domains with Circular Boundaries. Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 400-416. http://geodesic.mathdoc.fr/item/MZM_2014_95_3_a7/

[1] S. V. Bochkarev, “Suschestvovanie bazisa v prostranstve funktsii, analiticheskikh v kruge, i nekotorye svoistva sistemy Franklina”, Matem. sb., 95:1 (1974), 3–18 | MR | Zbl

[2] Z. Ciesielski, “Bases and approximation by splines”, Proceedings of the International Congress of Mathematicians, Vol. 2, Canad. Math. Congress, Montreal, Que., 1975, 47–51 | MR | Zbl

[3] Ju. N. Subbotin, “Approximative properties of splines”, Approximation Theory, Lecture Notes in Math., 556, Springer-Verlag, Berlin, 1976, 416–427 | DOI | MR | Zbl

[4] Yu. N. Subbotin, N. I. Chernykh, “Vspleski v prostranstvakh garmonicheskikh funktsii”, Izv. RAN. Ser. matem., 64:1 (2000), 145–174 | DOI | MR | Zbl

[5] Yu. N. Subbotin, N. I. Chernykh, “Vspleski periodicheskie, garmonicheskie i analiticheskie v kruge s netsentralnym otverstiem”, Tr. Mezhdunar. let. mat. shkoly S.B. Stechkina po teorii funktsii, Izd-vo TulGU, Tula, 2007, 129–149

[6] Yu. N. Subbotin, N. I. Chernykh, “Bazisy vspleskov v prostranstvakh analiticheskikh funktsii”, Teoriya priblizhenii. Garmonicheskii analiz, Sbornik statei, posvyaschennyi pamyati professora Sergeya Borisovicha Stechkina, Tr. MIAN, 219, Nauka, M., 1997, 340–355 | MR | Zbl

[7] Yu. N. Subbotin, N. I. Chernykh, “Bazisy vspleskov v prostranstvakh analiticheskikh v koltse funktsii”, Tr. Mezhdunar. let. mat. shkoly S.B. Stechkina po teorii funktsii, Izd-vo TulGU, Tula, 1999, 149–158

[8] Y. Meyer, Ondelettes et operateurs. I. OndeletsOndelettes, Actualités Math., Hermann, Paris, 1990 | MR | Zbl

[9] D. Offin, K. Oskolkov, “A note on orthonormal polynomial bases and wavelets”, Constr. Approx., 9:2-3 (1993), 319–325 | DOI | MR | Zbl

[10] U. Kheiman, P. Kennedi, Subgarmonicheskie funktsii, Mir, M., 1980 | MR | Zbl

[11] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR | Zbl

[12] S. M. Nikolskii, “Ob asimptoticheskom povedenii ostatka pri priblizhenii funktsii, udovletvoryayuschikh usloviyu Lipshitsa, summami Feiera”, Izv. AN SSSR. Ser. matem., 4:6 (1940), 501–508 | MR | Zbl

[13] N. P. Korneichuk, A. A. Ligun, V. G. Doronin, Approksimatsiya s ogranicheniyami, Naukova dumka, Kiev, 1982 | MR | Zbl