Geodesic
Wavelets in spaces of harmonic functions
Izvestiya. Mathematics , Tome 64 (2000) no. 1, pp. 143-171.

Voir la notice de l'article provenant de la source Math-Net.Ru

Using Meyer's bases of wavelets [1], we construct orthogonal bases of wavelets in the spaces $h_p$ $(1\leqslant p\leqslant \infty)$ of functions harmonic in the unit disc $|z|1$ or in the annulus $0\rho|z|1$. The partial sums of the Fourier series with respect to these bases possess approximating properties comparable with the best approximations by trigonometric polynomials. 
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Yu. N. Subbotin; N. I. Chernykh. Wavelets in spaces of harmonic functions. Izvestiya. Mathematics , Tome 64 (2000) no. 1, pp. 143-171. http://geodesic.mathdoc.fr/item/IM2_2000_64_1_a4/

[1] Meyer Y., “Ondelettes et operateurs. I: Ondelets”, Actualites Mathematiques, Hermann, Paris, 1990 | MR

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

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

[4] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Gosizdat, M.–L., 1952 | MR

[5] Garnet Dzh., Ogranichennye analiticheskie funktsii, Mir, M., 1984 | MR | Zbl

[6] Bochkarev S. V., “Suschestvovanie bazisa v prostranstve analiticheskikh v edinichnom kruge funktsii i nekotorye svoistva sistemy Franklina”, Matem. sb., 95 (137):1 (1974), 3–18 | Zbl

[7] Bochkarev S. V., “Postroenie polinomialnykh bazisov v konechnomernykh prostranstvakh analiticheskikh v kruge funktsii”, Tr. MIAN SSSR, 164, Nauka, M., 1983, 49–74 | MR | Zbl

[8] Bochkarev S. V., “Postroenie interpolyatsionnogo diadicheskogo bazisa v prostranstve nepreryvnykh funktsii na osnove yader Feiera”, Tr. MIAN SSSR, 172, Nauka, M., 1985, 29–59 | MR | Zbl

[9] Bourgain J., “Homogeneous polynomials on the ball and polynomial bases”, Israel J. Math., 68:3 (1989), 327–347 | DOI | MR | Zbl

[10] Woitaszczyk P., Wozniakowski K., Orthonormal polynomial basis in function spaces, Preprint 475, Inst. Math. PAS, 1990