Arkiv för Matematik

  • Ark. Mat.
  • Volume 18, Number 1-2 (1980), 107-116.

Removable singularities for analytic or subharmonic functions

Robert Kaufman and Jang-Mei Wu

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Abstract

In this paper, results on removable singularities for analytic functions, harmonic functions and subharmonic functions by Besicovitch, Carleson, and Shapiro are extended. In each theorem, we need not assume that f has the global property at any point, so we are able to allow dense sets of singularities. We do not state our results in terms of exceptional sets, but each one leads to a series of results implying that certain sets are removable for appropriate classes of functions.

Note

Partially supported by an NSF-Grant and an XL-Grant at Purdue respectively.

Article information

Source
Ark. Mat., Volume 18, Number 1-2 (1980), 107-116.

Dates
Received: 6 October 1978
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485896611

Digital Object Identifier
doi:10.1007/BF02384684

Mathematical Reviews number (MathSciNet)
MR608330

Zentralblatt MATH identifier
0444.30002

Rights
1980 © Institut Mittag-Leffler

Citation

Kaufman, Robert; Wu, Jang-Mei. Removable singularities for analytic or subharmonic functions. Ark. Mat. 18 (1980), no. 1-2, 107--116. doi:10.1007/BF02384684. https://projecteuclid.org/euclid.afm/1485896611


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References

  • Besicovitch, A., On sufficient conditions for a function to be analytic and on behavior of analytic functions in the neighborhood of non-isolated singular points, Proc. London Math. Soc. 2 (32) (1931), 1–9.
  • Carleson, L., On null-sets for continuous analytic functions, Arkiv Mat. 1 (1950), 311–318.
  • Carleson, L., Removable singularities of continuous harmonic functions in Rm, Math. Scand. 12 (1963), 15–18.
  • Carleson, L., Selected Problems on Exceptional Sets, Van Nostrand, 1967.
  • Shapiro, V. L., Subharmonic Functions and Hausdorff Measure, J. Diff. Equations 27 (1978), 28–45.
  • Stein, E. M., Singular Integrals and Differentiability properties of functions, Princeton University Press, 1970.