TY - JOUR

T1 - Multivariate sampling-type approximation

AU - Krivoshein, A.

AU - Skopina, M.

N1 - DOI: 10.1142/S0219530516500147

PY - 2017/7/1

Y1 - 2017/7/1

N2 - Approximation properties of the expansions ∑k ℤdLf(M-j.)(-k)φ(Mjx + k), where L is a linear differential operator and M is a matrix dilation, are studied. The sampling expansions are a special case of such differential expansions. Error estimations in Lp-norm, 2 ;le& p ;le, are given in terms of the Fourier transform of f. The approximation order depends on the smoothness of f, the order of L, the order of Strang-Fix condition for φ and M. A wide class of φ including both band-limited and compactly supported functions is considered, but a special condition of compatibility φ with L is required. Such differential expansions may be useful for engineers.

AB - Approximation properties of the expansions ∑k ℤdLf(M-j.)(-k)φ(Mjx + k), where L is a linear differential operator and M is a matrix dilation, are studied. The sampling expansions are a special case of such differential expansions. Error estimations in Lp-norm, 2 ;le& p ;le, are given in terms of the Fourier transform of f. The approximation order depends on the smoothness of f, the order of L, the order of Strang-Fix condition for φ and M. A wide class of φ including both band-limited and compactly supported functions is considered, but a special condition of compatibility φ with L is required. Such differential expansions may be useful for engineers.

KW - approximation order

KW - Generalized sampling expansions

KW - matrix dilation

KW - Strang-Fix condition

UR - http://www.scopus.com/inward/record.url?scp=84983407946&partnerID=8YFLogxK

U2 - 10.1142/S0219530516500147

DO - 10.1142/S0219530516500147

M3 - Article

AN - SCOPUS:84983407946

VL - 15

SP - 521

EP - 542

JO - Analysis and Applications

JF - Analysis and Applications

SN - 0219-5305

IS - 4

ER -