### Abstract

Original language | English |
---|---|

Pages (from-to) | 1276-1305 |

Number of pages | 30 |

Journal | Journal of Fourier Analysis and Applications |

Volume | 24 |

Issue number | 5 |

DOIs | |

Publication status | Published - Oct 2018 |

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### Scopus subject areas

- Analysis
- Mathematics(all)
- Applied Mathematics

### Cite this

*Journal of Fourier Analysis and Applications*,

*24*(5), 1276-1305. https://doi.org/10.1007/s00041-017-9559-1

}

*Journal of Fourier Analysis and Applications*, vol. 24, no. 5, pp. 1276-1305. https://doi.org/10.1007/s00041-017-9559-1

**Differential and Falsified Sampling Expansions.** / Kolomoitsev, Y.; Krivoshein, A.; Skopina, M.

Research output

TY - JOUR

T1 - Differential and Falsified Sampling Expansions

AU - Kolomoitsev, Y.

AU - Krivoshein, A.

AU - Skopina, M.

N1 - DOI: 10.1007/s00041-017-9559-1

PY - 2018/10

Y1 - 2018/10

N2 - Differential and falsified sampling expansions k. Zd ck.( M j x + k), where M is a matrix dilation, are studied. In the case of differential expansions, ck = L f ( M - j center dot)(- k), where L is an appropriate differential operator. For a large class of functions., the approximation order of differential expansions was recently studied. Some smoothness of the Fourier transform of. from this class is required. In the present paper, we obtain similar results for a class of band- limited functions. with the discontinuous Fourier transform. In the case of falsified expansions, ck is the mathematical expectation of random integral average of a signal f near the point M - j k. To estimate the approximation order of the falsified sampling expansions we compare them with the differential expansions. Error estimations in L p- norm are given in terms of the Fourier transform of f

AB - Differential and falsified sampling expansions k. Zd ck.( M j x + k), where M is a matrix dilation, are studied. In the case of differential expansions, ck = L f ( M - j center dot)(- k), where L is an appropriate differential operator. For a large class of functions., the approximation order of differential expansions was recently studied. Some smoothness of the Fourier transform of. from this class is required. In the present paper, we obtain similar results for a class of band- limited functions. with the discontinuous Fourier transform. In the case of falsified expansions, ck is the mathematical expectation of random integral average of a signal f near the point M - j k. To estimate the approximation order of the falsified sampling expansions we compare them with the differential expansions. Error estimations in L p- norm are given in terms of the Fourier transform of f

KW - Approximation order

KW - Differential expansion

KW - Falsified sampling expansion

KW - Matrix dilation

KW - Strang–Fix condition

UR - http://www.scopus.com/inward/record.url?scp=85028771798&partnerID=8YFLogxK

U2 - 10.1007/s00041-017-9559-1

DO - 10.1007/s00041-017-9559-1

M3 - Article

AN - SCOPUS:85028771798

VL - 24

SP - 1276

EP - 1305

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

SN - 1069-5869

IS - 5

ER -