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 thatf 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.
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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 inR m,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.
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Partially supported by an NSF-Grant and an XL-Grant at Purdue respectively.
An erratum to this article is available at http://dx.doi.org/10.1007/BF02384297.
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Kaufman, R., Wu, JM. Removable singularities for analytic or subharmonic functions. Ark. Mat. 18, 107–116 (1980). https://doi.org/10.1007/BF02384684
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DOI: https://doi.org/10.1007/BF02384684