Konstantin Yu. Osipenko

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Let Sβ := {z ∈ C : | Im z| < β} be a strip in the complex plane. For fixed integer r ≥ 0 let Hr ∞,β denote the class of 2π-periodic functions f , which are analytic in Sβ and satisfy |f(r)(z)| ≤ 1 in Sβ . Denote by Hr,R ∞,β the subset of functions from Hr ∞,β that are real-valued on the real axis. Given a function f ∈ Hr ∞,β , we try to recover f(ζ) at a(More)
We consider the problem of optimal recovery of solutions of the generalized heat equation in the unit ball. Information is given at two time instances, but inaccurate. The solution is to be constructed at some intermediate time. We provide the optimal error and present an algorithm which achieves this error level. The application of optimal recovery theory(More)
1. General setting Let T be a nonempty set, Σ be the σ -algebra of subsets of T , and μ be a nonnegative σ -additive measure on Σ . We denote by Lp(T , Σ, μ) (or simply Lp(T , μ)) the set of all Σ-measurable functions with values in R or in C for which ∥x(·)∥Lp(T ,μ) =  T |x(t)|p dμ(t) 1/p < ∞, 1 ≤ p < ∞, ∥x(·)∥L∞(T ,μ) = ess sup t∈T |x(t)| < ∞, p = ∞.(More)
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