Embedding of spaces and wavelet decomposition

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Embedding of spaces and wavelet decomposition. / Dem'yanovich, Yu K.

In: St. Petersburg Mathematical Journal, Vol. 31, No. 3, 2020, p. 435-453.

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

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Dem'yanovich, Yu K. / Embedding of spaces and wavelet decomposition. In: St. Petersburg Mathematical Journal. 2020 ; Vol. 31, No. 3. pp. 435-453.

BibTeX

@article{8e2307d2361c44d5bdea29ed46905c7d,

title = "Embedding of spaces and wavelet decomposition",

abstract = "Necessary and sufficient conditions of generalized smoothness (called pseudosmoothness) are found for coordinate functions of the finite element method (FEM). Embedding of FEM spaces on embedded subdivisions is discussed. Approximation relations on a differentiable manifold are considered. The concept of pseudosmoothness is formulated in terms of the coincidence of values for linear functionals on functions in question. The concept of maximum pseudosmoothness is introduced. Embedding criteria for spaces on embedded subdivisions are given. Wavelet expansion algorithms are developed for the spaces mentioned above.",

keywords = "Approximation relations, Finite element method, Functions on a manifold, Generalized smoothness, Minimal splines, Nesting of spaces, Wavelet expansions",

author = "Dem'yanovich, {Yu K.}",

note = "Funding Information: 2010 Mathematics Subject Classification. Primary 41A15. Key words and phrases. Approximation relations, generalized smoothness, nesting of spaces, wavelet expansions, minimal splines, finite element method, functions on a manifold. This work was partially supported by RFBR grant 15-01-008847. Publisher Copyright: {\textcopyright} 2020, American Mathematical Society. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2020",

doi = "10.1090/SPMJ/1607",

language = "English",

volume = "31",

pages = "435--453",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "3",

}

RIS

TY - JOUR

T1 - Embedding of spaces and wavelet decomposition

AU - Dem'yanovich, Yu K.

N1 - Funding Information: 2010 Mathematics Subject Classification. Primary 41A15. Key words and phrases. Approximation relations, generalized smoothness, nesting of spaces, wavelet expansions, minimal splines, finite element method, functions on a manifold. This work was partially supported by RFBR grant 15-01-008847. Publisher Copyright: © 2020, American Mathematical Society. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - Necessary and sufficient conditions of generalized smoothness (called pseudosmoothness) are found for coordinate functions of the finite element method (FEM). Embedding of FEM spaces on embedded subdivisions is discussed. Approximation relations on a differentiable manifold are considered. The concept of pseudosmoothness is formulated in terms of the coincidence of values for linear functionals on functions in question. The concept of maximum pseudosmoothness is introduced. Embedding criteria for spaces on embedded subdivisions are given. Wavelet expansion algorithms are developed for the spaces mentioned above.

AB - Necessary and sufficient conditions of generalized smoothness (called pseudosmoothness) are found for coordinate functions of the finite element method (FEM). Embedding of FEM spaces on embedded subdivisions is discussed. Approximation relations on a differentiable manifold are considered. The concept of pseudosmoothness is formulated in terms of the coincidence of values for linear functionals on functions in question. The concept of maximum pseudosmoothness is introduced. Embedding criteria for spaces on embedded subdivisions are given. Wavelet expansion algorithms are developed for the spaces mentioned above.

KW - Approximation relations

KW - Finite element method

KW - Functions on a manifold

KW - Generalized smoothness

KW - Minimal splines

KW - Nesting of spaces

KW - Wavelet expansions

UR - http://www.scopus.com/inward/record.url?scp=85085751763&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/e5fe8a42-4ce3-3253-918b-3fda8485a575/

U2 - 10.1090/SPMJ/1607

DO - 10.1090/SPMJ/1607

M3 - Article

AN - SCOPUS:85085751763

VL - 31

SP - 435

EP - 453

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 3

ER -

ID: 70501507