Approximation by periodic multivariate quasi-projection operators

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Approximation by periodic multivariate quasi-projection operators. / Kolomoitsev, Yu.; Krivoshein, A.; Skopina, M.

In: Journal of Mathematical Analysis and Applications, Vol. 489, No. 2, 124192, 15.09.2020.

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

Author

Kolomoitsev, Yu. ; Krivoshein, A. ; Skopina, M. / Approximation by periodic multivariate quasi-projection operators. In: Journal of Mathematical Analysis and Applications. 2020 ; Vol. 489, No. 2.

BibTeX

@article{993d605bf05b460aaafd17a513942692,

title = "Approximation by periodic multivariate quasi-projection operators",

abstract = "Approximation properties of periodic quasi-projection operators with matrix dilations are studied. Such operators are generated by a sequence of functions φj and a sequence of distributions/functions φ˜j. Error estimates for sampling-type quasi-projection operators are obtained under the periodic Strang-Fix conditions for φj and the compatibility conditions for φj and φ˜j. These estimates are given in terms of the Fourier coefficients of approximated functions and provide analogs of some known non-periodic results. Under some additional assumptions error estimates are given in other terms in particular using the best approximation. A number of examples are provided.",

keywords = "Best approximation, Error of approximation, Matrix dilation, Periodic quasi-projection operators, Periodic Strang-Fix conditions, Wiener's classes, INTERPOLATION, ORDER, SPACES, ERROR",

author = "Yu. Kolomoitsev and A. Krivoshein and M. Skopina",

year = "2020",

month = sep,

day = "15",

doi = "10.1016/j.jmaa.2020.124192",

language = "English",

volume = "489",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Elsevier",

number = "2",

}

RIS

TY - JOUR

T1 - Approximation by periodic multivariate quasi-projection operators

AU - Kolomoitsev, Yu.

AU - Krivoshein, A.

AU - Skopina, M.

PY - 2020/9/15

Y1 - 2020/9/15

N2 - Approximation properties of periodic quasi-projection operators with matrix dilations are studied. Such operators are generated by a sequence of functions φj and a sequence of distributions/functions φ˜j. Error estimates for sampling-type quasi-projection operators are obtained under the periodic Strang-Fix conditions for φj and the compatibility conditions for φj and φ˜j. These estimates are given in terms of the Fourier coefficients of approximated functions and provide analogs of some known non-periodic results. Under some additional assumptions error estimates are given in other terms in particular using the best approximation. A number of examples are provided.

AB - Approximation properties of periodic quasi-projection operators with matrix dilations are studied. Such operators are generated by a sequence of functions φj and a sequence of distributions/functions φ˜j. Error estimates for sampling-type quasi-projection operators are obtained under the periodic Strang-Fix conditions for φj and the compatibility conditions for φj and φ˜j. These estimates are given in terms of the Fourier coefficients of approximated functions and provide analogs of some known non-periodic results. Under some additional assumptions error estimates are given in other terms in particular using the best approximation. A number of examples are provided.

KW - Best approximation

KW - Error of approximation

KW - Matrix dilation

KW - Periodic quasi-projection operators

KW - Periodic Strang-Fix conditions

KW - Wiener's classes

KW - INTERPOLATION

KW - ORDER

KW - SPACES

KW - ERROR

UR - http://www.scopus.com/inward/record.url?scp=85089439058&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2020.124192

DO - 10.1016/j.jmaa.2020.124192

M3 - Article

AN - SCOPUS:85089439058

VL - 489

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

M1 - 124192

ER -

ID: 62158248