On multivariable Plancherel–Pólya inequality and truncation error upper bounds in irregular sampling

Abstract

In the note is shown that for the d-dimensional Bernstein functions class B_{varvec{sigma },d}^p,, p>0 the Plancherel–Pólya inequality holds with the constant which equals to the product of the constants occuring in the one-dimensional cases. Related truncation error upper bounds are precised in the irregular sampling restoration of functions in several variables.