We prove that the kernels of analytic functions of the form
satisfy Kushpel’s condition C y,2n starting from a certain number n h explicitly expressed via the parameter h of smoothness of the kernel. As a result, for all n ≥ n h , we establish lower bounds for the Kolmogorov widths d 2n in the space C of functional classes that can be represented in the form of convolutions of the kernel H h,β with functions φ⊥1 from the unit ball in the space L ∞ .
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 6, pp. 719–738, June, 2015.
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Bodenchuk, V.V., Serdyuk, A.S. Exact Values of Kolmogorov Widths for the Classes of Analytic Functions. I. Ukr Math J 67, 815–837 (2015). https://doi.org/10.1007/s11253-015-1116-y
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DOI: https://doi.org/10.1007/s11253-015-1116-y