Testing holomorphy on curves
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For a domain D ⊂ ℝ n we construct a continuous foliation of D into one-real-dimensional curves such that any function f ∈ C 1(D) which can be extended holomorphically into some neighborhood of each curve in the foliation will be holomorphic on D.
KeywordsHolomorphic Function Lipschitz Condition Limit Direction Complex Line Real Analytic Function
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- [FM]B. Fridman and D. Ma, Holomorphic functions on subsets of ℝ, Journal of the Mathematical Society of Japan, to appear.Google Scholar