Long, Jingfan; Fang, Gensun On uniform truncation error bounds and aliasing error for multidimensional sampling expansion. (English) Zbl 1137.94327 Sampl. Theory Signal Image Process. 2, No. 2, 103-115 (2003). Summary: Let \(B_v(\mathbb R^{n}), v=(v_1, \dots, v_n) \in \mathbb R^{n}_{+}\), be the set of entire functions of exponential type \(v\) bounded on \(\mathbb R^n\) and \(B^{r}_{p\theta}, 1 \leq p \leq \infty, 1 \leq \theta \leq \infty\), be the anisotropic Besov classes of functions. The uniform bounds of truncation error is estimated for \(f \in B_v(\mathbb R^{n})\) and satisfying the following decay condition: \[ |f(x)| \leq \frac{A}{{(1+|x|)}^\delta}, x=(x_1, \dots, x_n) \in \mathbb R^n \] , associated with the Shannon multidimensional sampling representation. The bounds of aliasing error for \(f \in B^{r}_{\infty \theta} (\mathbb R^n)\) and satisfying the same decay condition as above is also evaluated. Cited in 3 Documents MSC: 94A20 Sampling theory in information and communication theory 41A25 Rate of convergence, degree of approximation 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) Keywords:truncation error; band-limited function; anisotropic Besov class of function PDFBibTeX XMLCite \textit{J. Long} and \textit{G. Fang}, Sampl. Theory Signal Image Process. 2, No. 2, 103--115 (2003; Zbl 1137.94327)