Harmonic analysis in a multiply-connected domain. I

S. I. Fedorov

Sbornik. Mathematics, Tome 70 (1991) no. 1, pp. 263-296

Résumé

The purpose of this article is to construct harmonic analysis in a finitely-connected plane domain $\Omega_+$ bounded by $n$ piecewise analytic curves $\Gamma_1,\dots,\Gamma_n$, $\bigcup\limits_{k=1}^n\Gamma_k=\Gamma=\partial\Omega_+$.

Bibliographie

[1] Nikolskii N. K., Lektsii ob operatore sdviga, Nauka, M., 1980 | MR

[2] Nikolskii N. K., Pavlov B. S., “Razlozheniya po sobstvennym vektoram neunitarnykh operatorov i kharakteristicheskaya funktsiya”, Zap. nauchn. semin. LOMI, 11 (1968), 150–203 | MR

[3] Sekefalvi-Nad B., Foyash Ch., Garmonicheskii analiz operatorov v gilbertovom prostranstve, Mir, M., 1970 | MR

[4] Laks P., Fillips R., Teoriya rasseyaniya, Mir, M., 1971 | MR

[5] Fisher S., Functon theory of planar domains, John Wiley Sons, New York, Toronto, 1983 | MR | Zbl

[6] Forelli F., “Bounded holomorphic functions and projections”, Illinois J. Math., 10 (1966), 367–380 | MR | Zbl

[7] Earle C. J., Marden A., “On Poincare series with application to $H^p$ spaces on bordered Riemann surfaces”, Ill. J. Math., 13:1 (1969), 202–219 | MR | Zbl

[8] Voichek M., “Ideals and invariant subspaces of analitc functions”, Trans. Amer. Math. Soc., 111 (1964), 493–512 | DOI | MR

[9] Voichek M., Zalcman L., “Inner and outer functions on Riemann surfaces”, Proc. Amer. Math. Soc., 16 (1965), 1200–1204 | DOI | MR

[10] Hasumi M., Hardy classes on infinitely connected Riemann surfaces, Lect. Notes in Math., no. 1027, 1983 | MR

[11] Nevill C. W., Hardy classes on infinitely connected open Riemann surfaces, Mem. Amer. Math. Soc., no. 160, 1975 | MR

[12] Sarson D., The $H^p$ spaces of an annulus, Mem. Amer. Math. Soc., no. 56, 1966

[13] Alling N. L., “Extensions of meromorphic function rings over noncompact Riemann surfaces, I”, Math. Z., 79:4 (1965), 273–299 | DOI | MR

[14] Stout E. L., “On some algebras of analitic functions on finite open Riemann surfaces”, Math. Z., 92:5 (1966), 366–379 | DOI | MR

[15] Stout E. L., “Bounded holomorphic functions on finite Riemann surfaces”, Trans. Amer. Math. Soc., 120:11 (1965), 255–285 | DOI | MR

[16] Pavlov B. S., Fedorov S. I., “Gruppa sdvigov i garmonicheskii analiz na rimanovoi poverkhnosti roda odin”, Algebra i Analiz, 1:2 (1989), 132–168 | MR | Zbl

[17] Springer Dzh., Vvedenie v teoriyu rimanovykh poverkhnostei, IL, M., 1960

[18] Shiffer M., Spenser D. K., Funktsionaly na konechnykh rimanovykh poverkhnostyakh, IL, M., 1957

[19] Akhiezer N. I., “Ob ortogonalnykh mnogochlenakh na neskolkikh intervalakh”, DAN SSSR, 134:1 (1960), 9–12 | Zbl

[20] Akhiezer N. I., Tomchuk Yu. Ya., “K teorii ortogonalnykh mnogochlenov na neskolkikh intervalakh”, DAN SSSR, 138:4 (1961), 743–746 | Zbl

[21] Tomchuk Yu. Ya., “Ortogonalnye mnogochleny na sisteme intervalov chislovoi osi”, Zap. Kharkovskogo mat. obsch., ser. 4, 29 (1963), 97–128

[22] Rudin W., “Analitic functions of class $H^p$”, Trans. Amer. Math. Soc., 78 (1955), 46–66 | DOI | MR | Zbl

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

[24] Khavinson S. Ya., “Teoriya faktorizatsii odnoznachnykh analiticheskikh funktsii na kompaktnykh rimanovykh poverkhnostyakh s kraem”, UMN, 44:4(268) (1989), 155–190 | MR

[25] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu nesamosopryazhennykh operatorov, Nauka, M., 1965