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On multivariable Plancherel–Pólya inequality and truncation error upper bounds in irregular sampling
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AbstractIn the note is shown that for thed-dimensional Bernstein functions class$$B_{\varvec{\sigma },d}^p,\, p>0$$Bσ,dp,p>0the 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.
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Title: On multivariable Plancherel–Pólya inequality and truncation error upper bounds in irregular sampling
Description:
AbstractIn the note is shown that for thed-dimensional Bernstein functions class$$B_{\varvec{\sigma },d}^p,\, p>0$$Bσ,dp,p>0the 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.
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