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Multivariate sampling-type approximation. / Krivoshein, A.; Skopina, M.

In: Analysis and Applications, Vol. 15, No. 4, 01.07.2017, p. 521-542.

Research output: Contribution to journal › Article › peer-review

Harvard

Krivoshein, A & Skopina, M 2017, 'Multivariate sampling-type approximation', Analysis and Applications, vol. 15, no. 4, pp. 521-542. https://doi.org/10.1142/S0219530516500147

APA

Krivoshein, A., & Skopina, M. (2017). Multivariate sampling-type approximation. Analysis and Applications, 15(4), 521-542. https://doi.org/10.1142/S0219530516500147

Vancouver

Krivoshein A, Skopina M. Multivariate sampling-type approximation. Analysis and Applications. 2017 Jul 1;15(4):521-542. https://doi.org/10.1142/S0219530516500147

Author

Krivoshein, A. ; Skopina, M. / Multivariate sampling-type approximation. In: Analysis and Applications. 2017 ; Vol. 15, No. 4. pp. 521-542.

BibTeX

@article{c7c8dd8c2d4a4a2f99980a2de6c64342,
title = "Multivariate sampling-type approximation",
abstract = "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.",
keywords = "approximation order, Generalized sampling expansions, matrix dilation, Strang-Fix condition",
author = "A. Krivoshein and M. Skopina",
note = "DOI: 10.1142/S0219530516500147",
year = "2017",
month = jul,
day = "1",
doi = "10.1142/S0219530516500147",
language = "English",
volume = "15",
pages = "521--542",
journal = "Analysis and Applications",
issn = "0219-5305",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",
number = "4",

}

RIS

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 -

ID: 15680094