Geodesic
Extension of matrices with entries in $H^\infty$ on coverings of Riemann surfaces of finite type
Algebra i analiz, Tome 21 (2009) no. 3, pp. 79-92.

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

The paper continues an earlier work of the author. An extension theorem is proved for matrices with entries in the algebra of bounded holomorphic functions defined on an unbranched covering of a Caratheodory hyperbolic Riemann surface of finite type.
Keywords: corona theorem, bounded holomorphic function, covering, Riemann surface of finite type. 
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A. Brudnyi. Extension of matrices with entries in $H^\infty$ on coverings of Riemann surfaces of finite type. Algebra i analiz, Tome 21 (2009) no. 3, pp. 79-92. http://geodesic.mathdoc.fr/item/AA_2009_21_3_a2/

[1] Barrett D. E., Diller J., “A new construction of Riemann surfaces with corona”, J. Geom. Anal., 8 (1998), 341–347 | MR | Zbl

[2] Brudnyi A., “Projections in the space $H^\infty$ and the corona theorem for subdomains of coverings of finite bordered Riemann surfaces”, Ark. Mat., 42:1 (2004), 31–59 | MR | Zbl

[3] Brudnyi A., “Grauert- and Lax–Halmos-type theorems and extension of matrices with entries in $H^\infty$”, J. Funct. Anal., 206 (2004), 87–108 | DOI | MR | Zbl

[4] Brudnyi A., “A uniqueness property for $H^\infty$ on coverings of projective manifolds”, Michigan Math. J., 51:3 (2003), 503–507 | DOI | MR | Zbl

[5] Brudnyi A., “Corona theorem for $H^\infty$ on coverings of Riemann surfaces of finite type”, Michigan Math. J., 56 (2008), 283–299 | DOI | MR | Zbl

[6] Brudnyi A., “Matrix-valued corona theorem for multiply connected domains”, Indiana Univ. Math. J., 49 (2000), 1405–1410 | DOI | MR | Zbl

[7] Carleson L., “Interpolation of bounded analytic functions and the corona problem”, Ann. of Math. (2), 76 (1962), 547–559 | DOI | MR | Zbl

[8] Eilenberg S., Steenrod N., Foundations of algebraic topology, Princeton Univ. Press, Princeton, NJ, 1952 | MR | Zbl

[9] Freudenthal H., “Über dimensionserhöhende stetige Abbildungen”, Sitzber. Preus. Akad. Wiss., 5 (1932), 34–38 | Zbl

[10] Garnett J. B., Bounded analytic functions, Pure Appl. Math., 96, Acad. Press, New York–London, 1981 | MR | Zbl

[11] Gamelin T. W., Uniform algebras and Jensen measures, London Math. Soc. Lecture Notes Ser., 32, Cambridge Univ. Press, Cambridge–New York, 1978 | MR | Zbl

[12] Garnett J. B., Jones P. W., “The corona theorem for Denjoy domains”, Acta Math., 155 (1985), 27–40 | DOI | MR | Zbl

[13] Husemoller D., Fibre bundles, McGraw-Hill Book Co., New York etc., 1966 | MR | Zbl

[14] Jones P. W., Marshall D., “Critical points of Green's functions, harmonic measure, and the corona problem”, Ark. Mat., 23 (1985), 281–314 | DOI | MR | Zbl

[15] Nagami K., Dimension theory, Pure Appl. Math., 37, Acad. Press, New York–London, 1970 | MR

[16] Lárusson F., “Holomorphic functions of slow growth on nested covering spaces of compact manifolds”, Canad. J. Math., 52 (2000), 982–998 | MR | Zbl

[17] Lin V. Ya., “Golomorfnye rassloeniya i mnogoznachnye funktsii ot elementov banakhovoi algebry”, Funkts. anal. i ego pril., 7:2 (1973), 43–51 | MR | Zbl

[18] Moore C. N., “The corona theorem for domains whose boundary lies in a smooth curve”, Proc. Amer. Math. Soc., 100:2 (1987), 266–270 | DOI | MR | Zbl

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

[20] Tolokonnikov V., “Extension problem to an invertible matrix”, Proc. Amer. Math. Soc., 117:4 (1993), 1023–1030 | DOI | MR | Zbl