, mE>0 It is shown that (even in the case when E is nowhere dense in
) there exist functions f, analytic in
and satisfying some strong additional conditions (for example, like: the Taylor series of the function f with center at the origin converges uniformly in the circle
, while the boundary values of the function
coincide with some function of the form
, where g ε C (T),
is the orthogonal projection from L2 onto h − 2 ). Moreover, one establishes theorems on the free interpolation by such functions, showing that they are indeed “very many.”
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 107, pp. 71–88, 1982.
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Kislyakov, S.V. More on free interpolation by functions which are regular outside a prescribed set. J Math Sci 36, 342–352 (1987). https://doi.org/10.1007/BF01839606
- Taylor Series
- Additional Condition
- Orthogonal Projection
- Free Interpolation