Geodesic
Approximation of the Hardy–Sobolev class of functions analytic in a half-plane by entire functions of exponential type
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 18-30
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We study the value $\mathcal E_\sigma(H^p_n)_{H^p}$ of the best approximation in the norm of the Hardy space $H^p$ for $1\le p\le\infty$ of the Hardy–Sobolev class $H_n^p$ of functions analytic in a half-plane with bounded $H^p$-norm of the $n$th-order derivative by entire functions of exponential type not exceeding $\sigma$. The equality $\mathcal E_\sigma(H^p_n)_{H^p}=\sigma^{-n}$ is proved. A linear method providing the best approximation of the class is constructed.
Keywords: Hardy class, approximation of functions, entire functions of exponential type. 
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R. R. Akopyan. Approximation of the Hardy–Sobolev class of functions analytic in a half-plane by entire functions of exponential type. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 18-30. http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a1/

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