Corpus ID: 54058138

BOUNDED HOLOMORPHIC FUNCTIONS ON FINITE RIEMANN SURFACES

@inproceedings{STOUTi2010BOUNDEDHF,
  title={BOUNDED HOLOMORPHIC FUNCTIONS ON FINITE RIEMANN SURFACES},
  author={E. L. STOUTi},
  year={2010}
}
In §2, we use this theorem to establish an analogous result in the setting of finite open Riemann surfaces. §§3 and 4 consider certain questions which arise naturally in the course of the proof of this generalization. We mention that the chief result of §2, Theorem 2.6, has been obtained independently by N. L. Ailing [3] who has used methods more highly algebraic than ours. The second matter we shall be concerned with is that of interpolation. If R is a Riemann surface and if £ is a subset of R… Expand
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References

SHOWING 1-10 OF 15 REFERENCES
Two theorems concerning functions holomorphic on multiply connected domains
1. Let £2 be a finitely connected plane domain whose boundary, d£2, consists of the circles To, I \ , • • • , Tw. We assume Ty lies in the interior of T0 for j= 1, 2, • • • , n. Let A0 be theExpand
A proof of the Corona conjecture for finite open Riemann surfaces
By a finite open Riemann surface is meant a proper, open, connected subset of a compact Riemann surface W whose boundary T is also the boundary of W— X and consists of a finite number of closedExpand
An Interpolation Problem for Bounded Analytic Functions
be possible for a given sequence of points {zv}, I z, 1, and an analytic function f(z) in I z i < 1, I f(z) I _ 1. The result is, however, very implicit ancd gives in a concrete situation very littleExpand
Introduction to Riemann Surfaces
Introduction: 1-1 Algebraic functions and Riemann surfaces 1-2 Plane fluid flows 1-3 Fluid flows on surfaces 1-4 Regular potentials 1-5 Meromorphic functions 1-6 Function theory on a torus GeneralExpand
Open Riemann surfaces and extremal problems on compact subregions
Royden, The boundary values of analytic and harmonic functions
  • Math. Z
  • 1962
and F
  • Sommer, Theorie der analytischen Funktionen, Springer-Verlag, Berlin,
  • 1955
Fundamental polygons of fuchsian and fuchsoid groups
Banach Spaces of Analytic Functions
Riemann surfaces, Princeton Univ
  • Press, Princeton, N. J.,
  • 1960
...
1
2
...