Uniform approximation on the real axes by functions harmonic in a stripe and having optimal growth
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Norair Arakelian
Let Sh be a stripe of the width 2h, symmetric with respect to the real axes ℝ. The aim of this paper is to solve (for sufficiently smooth functions on ℝ) the problem of uniform approximation on ℝ by functions harmonic on Sh and having optimal growth at infinity (see Theorems 1.3–1.4). These are direct results of Jackson type, where the mentioned growth is expressed in the terms of the growth of functions to be approximated and their structural properties. The analogous approximation problems on R by functions holomorphic on Sh have been discussed earlier by M. V. Keldish and other authors (see [1]–[4]). The methods used here are modifications and adaptations of those developed in [3]. In addition, a Bernstein type converse result is also presented (see 1.6).
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Articles in the same Issue
- In memoriam Gerald Schmieder
- A general cross theorem with singularities
- Bounded pointwise approximation on open Riemann surfaces
- Generalized Fourier expansion in kernels of convolution operators on Fourier hyperfunctions
- Stein's extension operator for sets with Lipγ-boundary
- On some representation formulas involving moduli of Blaschke products
- Universal (pluri)subharmonic functions
- Uniform approximation on the real axes by functions harmonic in a stripe and having optimal growth
- Univalence of a complex linear combination of two extremal parallel slit mappings
- Lacunary (R, p, M)-summability
- MacLane functions with prescribed zeros and interpolation properties
- Reasoning and proof in the mathematics classroom
