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Start date: 1990 × Publisher: Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach × Subject: Bernstein space ×

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    Near critical density irregular sampling in Bernstein spaces
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2013) Olevskii, Alexander; Ulanovskii, Alexander
    We obtain sharp estimates for the sampling constants in Bernstein spaces when the density of the sampling set is near the critical value.
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    Approximation of discrete functions and size of spectrum
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Olevskii, Alexander; Ulanovskii, Alexander
    Let Λ⊂R be a uniformly discrete sequence and S⊂R a compact set. We prove that if there exists a bounded sequence of functions in Paley-Wiener space PWs, which approximates δ-functions on Λ with l2-error d, then measure(S)≥2π(1−d2)D+(Λ). This estimate is sharp for every d. Analogous estimate holds when the norms of approximating functions have a moderate growth, and we find a sharp growth restriction.