Standard

Approximation by frame-like multiwavelets. / Кривошеин, Александр Владимирович.

In: Analysis and Applications, Vol. 22, No. 5, 01.07.2024, p. 881-911.

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

Harvard

Кривошеин, АВ 2024, 'Approximation by frame-like multiwavelets', Analysis and Applications, vol. 22, no. 5, pp. 881-911. https://doi.org/10.1142/S0219530524500052

APA

Кривошеин, А. В. (2024). Approximation by frame-like multiwavelets. Analysis and Applications, 22(5), 881-911. https://doi.org/10.1142/S0219530524500052

Vancouver

Кривошеин АВ. Approximation by frame-like multiwavelets. Analysis and Applications. 2024 Jul 1;22(5):881-911. https://doi.org/10.1142/S0219530524500052

Author

Кривошеин, Александр Владимирович. / Approximation by frame-like multiwavelets. In: Analysis and Applications. 2024 ; Vol. 22, No. 5. pp. 881-911.

BibTeX

@article{339f3dd058144fdb8fc5786ae6886cb8,
title = "Approximation by frame-like multiwavelets",
abstract = "Approximation properties of multivariate quasi-projection operators Qj(f,Φ,Φ˜) generated by vectors of compactly supported functions Φ, Φ˜ are studied. Error estimates in L2-norm are obtained for a wide class of such operators. For refinable function vectors Φ, Φ˜ quasi-projection operators are related to dual multiwavelet systems. Although the general scheme for the construction of dual multiwavelet frames in the multivariate case is known, its realization in practice is a difficult task because of the necessity of providing some additional properties. The notion of frame-like multiwavelets is a relaxed version of multiwavelet frames. Frame-like multiwavelets retain frame-type decompositions waiving the usual frame condition. This simplifies the problem of frame-like multiwavelets construction. Approximation properties of frame-like multiwavelets are established. Algorithms for constructing frame-like multiwavelets with the desired approximation order are suggested.",
keywords = "Multivariate multiwavelet systems, approximation order, Quasi-projection operator, refinable function vector, matrix mask, frame-like multiwavelets, Multivariate multiwavelet systems, approximation order, frame-like multiwavelets, matrix mask, quasi-projection operator, refinable function vector",
author = "Кривошеин, {Александр Владимирович}",
year = "2024",
month = jul,
day = "1",
doi = "10.1142/S0219530524500052",
language = "English",
volume = "22",
pages = "881--911",
journal = "Analysis and Applications",
issn = "0219-5305",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",
number = "5",

}

RIS

TY - JOUR

T1 - Approximation by frame-like multiwavelets

AU - Кривошеин, Александр Владимирович

PY - 2024/7/1

Y1 - 2024/7/1

N2 - Approximation properties of multivariate quasi-projection operators Qj(f,Φ,Φ˜) generated by vectors of compactly supported functions Φ, Φ˜ are studied. Error estimates in L2-norm are obtained for a wide class of such operators. For refinable function vectors Φ, Φ˜ quasi-projection operators are related to dual multiwavelet systems. Although the general scheme for the construction of dual multiwavelet frames in the multivariate case is known, its realization in practice is a difficult task because of the necessity of providing some additional properties. The notion of frame-like multiwavelets is a relaxed version of multiwavelet frames. Frame-like multiwavelets retain frame-type decompositions waiving the usual frame condition. This simplifies the problem of frame-like multiwavelets construction. Approximation properties of frame-like multiwavelets are established. Algorithms for constructing frame-like multiwavelets with the desired approximation order are suggested.

AB - Approximation properties of multivariate quasi-projection operators Qj(f,Φ,Φ˜) generated by vectors of compactly supported functions Φ, Φ˜ are studied. Error estimates in L2-norm are obtained for a wide class of such operators. For refinable function vectors Φ, Φ˜ quasi-projection operators are related to dual multiwavelet systems. Although the general scheme for the construction of dual multiwavelet frames in the multivariate case is known, its realization in practice is a difficult task because of the necessity of providing some additional properties. The notion of frame-like multiwavelets is a relaxed version of multiwavelet frames. Frame-like multiwavelets retain frame-type decompositions waiving the usual frame condition. This simplifies the problem of frame-like multiwavelets construction. Approximation properties of frame-like multiwavelets are established. Algorithms for constructing frame-like multiwavelets with the desired approximation order are suggested.

KW - Multivariate multiwavelet systems

KW - approximation order

KW - Quasi-projection operator

KW - refinable function vector

KW - matrix mask

KW - frame-like multiwavelets

KW - Multivariate multiwavelet systems

KW - approximation order

KW - frame-like multiwavelets

KW - matrix mask

KW - quasi-projection operator

KW - refinable function vector

UR - https://www.mendeley.com/catalogue/100415f4-2ae6-37f1-80c9-225e111e2f44/

U2 - 10.1142/S0219530524500052

DO - 10.1142/S0219530524500052

M3 - Article

VL - 22

SP - 881

EP - 911

JO - Analysis and Applications

JF - Analysis and Applications

SN - 0219-5305

IS - 5

ER -

ID: 119365485