Peak-interpolating curves for A(O) for finite-type domains in C2

• Autores: Gautam Bharali
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 218, Nº 2, 2005, págs. 283-298
• Idioma: inglés
• DOI: 10.2140/pjm.2005.218.283
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• Resumen

  • Let O be a bounded, weakly pseudoconvex domain in C2, having smooth boundary. A(O) is the algebra of all functions holomorphic in O and continuous up to the boundary. A smooth curve C ? ?O is said to be complex-tangential if Tp(C) lies in the maximal complex subspace of Tp(?O) for each p in C. We show that if C is complex-tangential and ?O is of constant type along C, then every compact subset of C is a peak-interpolation set for A(O). Furthermore, we show that if ?O is real-analytic and C is an arbitrary real-analytic, complex-tangential curve in ?O, compact subsets of C are peak-interpolation sets for A(O).