TY - GEN

T1 - Around Kotelnikov-Shannon formula

AU - Kolomoitsev, Yurii

AU - Skopina, Maria

PY - 2017/9/1

Y1 - 2017/9/1

N2 - Approximation properties of multivariate sampling-type expansions with matrix dilation are studied. In particular, we investigate the expansions whose coefficients are the sampled values of some linear combination of the approximated function f and its derivatives. The error estimation in Lp-norm, 2 ≤ p ≤ ∞, is given in terms of the Fourier transform of f for this case. Another class of expansions includes those whose coefficients are integral averages of f near the nodes. The error estimation in Lp-norm, 1 < p < ∞, is given in terms of the moduli of smoothness of f for this case.

AB - Approximation properties of multivariate sampling-type expansions with matrix dilation are studied. In particular, we investigate the expansions whose coefficients are the sampled values of some linear combination of the approximated function f and its derivatives. The error estimation in Lp-norm, 2 ≤ p ≤ ∞, is given in terms of the Fourier transform of f for this case. Another class of expansions includes those whose coefficients are integral averages of f near the nodes. The error estimation in Lp-norm, 1 < p < ∞, is given in terms of the moduli of smoothness of f for this case.

UR - http://www.scopus.com/inward/record.url?scp=85031695139&partnerID=8YFLogxK

U2 - 10.1109/SAMPTA.2017.8024385

DO - 10.1109/SAMPTA.2017.8024385

M3 - Conference contribution

AN - SCOPUS:85031695139

SP - 279

EP - 282

BT - 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017

A2 - Anbarjafari, Gholamreza

A2 - Kivinukk, Andi

A2 - Tamberg, Gert

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 12th International Conference on Sampling Theory and Applications, SampTA 2017

Y2 - 3 July 2017 through 7 July 2017

ER -