Nonclassical interpolation in spaces of analytic functions smooth up to the boundary
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One considers the following problem. Let X be the space of smooth functions on the circumference and let Y be the space of functions analytic in the disk and smooth up to the boundary. One has to find necessary and sufficient conditions on the closed subset E of the circumference that ensure the inclusionX¦E⊂y¦E. The problem is solved in the case when the space X is a Carleman class and Y is either an analytic Carleman class having weaker smoothness properties than X, or a Hölder class As with arbitrary exponent s.
KeywordsAnalytic Function Smooth Function Closed Subset Smoothness Property Carleman Class
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