In Mergelyan type approximation we uniformly approximate functions on compact sets K by polynomials or rational functions or holomorphic functions on varying open sets containing K. In the present paper we consider analogous approximation, where uniform convergence on K is replaced by uniform approximation on K of all order derivatives.
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Dedicated to Professor Paul M. Gauthier on the occasion of his 80th birthday.
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Communicated by Adrian Constantin.
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Armeniakos, S., Kotsovolis, G. & Nestoridis, V. Approximation of functions and all derivatives on compact sets. Monatsh Math (2021). https://doi.org/10.1007/s00605-021-01604-x
- Mergelyan theorem
- Uniform approximation of all order derivatives
- \(C^\infty \)
- \(A^\infty \)
- Holomorphic functions
- Completion of a metric space
Mathematics Subject Classification