A Remark on Fine Differentiability |
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Authors: | Roman Lávička |
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Institution: | (1) Mathematical Institute, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic |
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Abstract: | In 7], B. Fuglede has proved that finely holomorphic functions on a finely open subset U of the complex plane C are finely locally extendable to usual continuously differentiable functions. We shall adopt B. Fuglede’s approach to show
that the same remains true even for functions which have only finely continuous fine differential on U. In higher dimensions, an analogous result may be obtained and the result can be applied to finely monogenic functions which
were introduced recently as a higher dimensional analogue of finely holomorphic functions.
I acknowledge the financial support from the grant GA 201/05/2117. This work is also a part of the research plan MSM 0021620839,
which is financed by the Ministry of Education of the Czech Republic. |
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Keywords: | Primary 31C40 Secondary 30G12 30G35 |
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