Differential and Falsified Sampling Expansions

Y. Kolomoitsev, A. Krivoshein, M. Skopina

Research output

5 Citations (Scopus)

Abstract

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
Original languageEnglish
Pages (from-to)1276-1305
Number of pages30
JournalJournal of Fourier Analysis and Applications
Volume24
Issue number5
DOIs
Publication statusPublished - Oct 2018

Fingerprint

Sampling
Fourier transform
Fourier transforms
Order of Approximation
Band-limited Functions
Lp-norm
Error Estimation
Dilation
Error analysis
Mathematical operators
Differential operator
Smoothness
Estimate
Class

Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Applied Mathematics

Cite this

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abstract = "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",
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T1 - Differential and Falsified Sampling Expansions

AU - Kolomoitsev, Y.

AU - Krivoshein, A.

AU - Skopina, M.

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