Universal truncation error upper bounds in irregular sampling restoration

The classical WKS sampling theorem has been extended to the case of nonuniform sampling by numerous authors. For detailed information on the theory and its numerous applications, we refer to the book [15]. Most known irregular sampling results deal with Paley–Wiener functions which have L2(R) restrictions on the real line. It seems that the best known nonuniform WKS sampling results for entire functions in Lp–spaces were given in [10, 11]. There are no multidimensional Lp–WKS sampling theorems with precise truncation error estimates in open literature. However, explicit truncation error upper bounds in multidimensional WKS reconstructions are of great importance in signal and image processing. Alternative reconstruction approaches for irregular sampling problems were developed in [1, 4, 5]. However, due to long traditions the WKS type reconstructions still play key role in applied signal and image processing. New numerical methods for quick sinc–series summations (see, for example, [7]) let more efficient usage of WKS formulae than before. On the other hand WKS type results are important not only because of signal processing applications. WKS theorems are equivalent