engleski

Universal truncation error upper bounds in sampling restoration

The multidimensional analogue of the Plancherel-P\'olya inequality is obtained, and the extremal properties of series of "sinc" functions are investigated. Then universal (pointwise uniform and time shifted) truncation error upper bounds for the WKS uniform, regular sampling restoration sum for Bernstein classes $B_{;\pi, d};^q, q>1, d\in \mathbb N$$ are established, when the decay rate of the sampled functions is unknown.

Plancherel-P\'olya inequality; WKS sampling theorem; uniform sampling; truncation error upper bound

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