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Approximations of classes \( B_{p,{{\theta }}}^\Omega \) of functions of many variables by entire functions in the space L q (Rd)

Exact-order estimates are obtained for the best approximations of the classes \( B_{p,{{\theta }}}^\Omega \) of functions of many variables by entire functions of the exponential type in the space \( {L_q}\left( {{\mathbb{R}^d}} \right) \).

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Author information

Correspondence to S. Ya. Yanchenko.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 1, pp. 123–135, January, 2010.

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Yanchenko, S.Y. Approximations of classes \( B_{p,{{\theta }}}^\Omega \) of functions of many variables by entire functions in the space L q (Rd). Ukr Math J 62, 136–150 (2010). https://doi.org/10.1007/s11253-010-0338-2

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Keywords

  • Lower Bound
  • Entire Function
  • Periodic Function
  • Exponential Type
  • Periodic Case