Geodesic
On a sampling expansion with partial derivatives for functions of several variables
Filomat, Tome 34 (2020) no. 10, p. 3339

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Let B p σ , 1 ≤ p ∞, σ > 0, denote the space of all f ∈ L p (R) such that the Fourier transform of f (in the sense of distributions) vanishes outside [−σ , σ ]. The classical sampling theorem states that each f ∈ B p σ may be reconstructed exactly from its sample values at equispaced sampling points {πm/σ } m∈Z spaced by π/σ. Reconstruction is also possible from sample values at sampling points {πθ m/σ } m with certain 1 θ ≤ 2 if we know f (θ πm/σ) and f (θ πm/σ), m ∈ Z. In this paper we present sampling series for functions of several variables. These series involves samples of functions and their partial derivatives.
DOI : 10.2298/FIL2010339N
Classification : 41A05, 41A63, 32A15
Keywords: Bernstein’s spaces, Entire functions, Sampling series, Multidimensional sampling with derivatives 
Saulius Norvidas. On a sampling expansion with partial derivatives for functions of several variables. Filomat, Tome 34 (2020) no. 10, p. 3339 . doi: 10.2298/FIL2010339N
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     author = {Saulius Norvidas},
     title = {On a sampling expansion with partial derivatives for functions of several variables},
     journal = {Filomat},
     pages = {3339 },
     year = {2020},
     volume = {34},
     number = {10},
     doi = {10.2298/FIL2010339N},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2010339N/}
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