Vol. 83, No. 1, 1979

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The Rudin kernels on an arbitrary domain

Saburou Saitoh

Vol. 83 (1979), No. 1, 273–284

Let {Gn} (G0 x,t) denote a regular exhaustion of an arbitrary domain G in the complex plane. For fixed x, t(G), let Rt(n)(z,x), Lt(n)(z,x) and Lt(n)(z,x) denote the Rudin kernels of Gn, respectively. The convergence of the sequences {Rt(n)(z,x)}, {Lt(n)(z,x)} and {Lt(n)(z,x)} is discussed and some properties with respect to their limit functions are investigated. In the final Section, it is pointed oul that in the case of an arbitrary hyperbolic Riemann surface, the circumstances are quite different, in general.

Mathematical Subject Classification 2000
Primary: 30C35
Secondary: 30F99
Received: 1 July 1974
Published: 1 July 1979
Saburou Saitoh