On the Constants in the Inverse Theorems for the Norms of Derivatives

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On the Constants in the Inverse Theorems for the Norms of Derivatives. / Vinogradov, O. L.

In: Siberian Mathematical Journal, Vol. 63, No. 3, 05.2022, p. 438-450.

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

BibTeX

@article{575d2af27b07435dafa606018494bfe6,

title = "On the Constants in the Inverse Theorems for the Norms of Derivatives",

abstract = "We propose a new method for proving the classical inverse theoremsof the theory of approximation by trigonometric polynomials and entirefunctions of exponential type. The method is based on the constructionof identities expressing the derivatives of a function itself and of itstrigonometrical conjugate in terms of convolution operators. As a consequence,we reduce the constants in the estimates of the norms of the derivativesin terms of best approximations.",

keywords = "517.5, conjugate function, inverse theorems, sharp constants",

author = "Vinogradov, {O. L.}",

note = "Publisher Copyright: {\textcopyright} 2022, Pleiades Publishing, Ltd.",

year = "2022",

month = may,

doi = "10.1134/s0037446622030053",

language = "English",

volume = "63",

pages = "438--450",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - On the Constants in the Inverse Theorems for the Norms of Derivatives

AU - Vinogradov, O. L.

PY - 2022/5

Y1 - 2022/5

N2 - We propose a new method for proving the classical inverse theoremsof the theory of approximation by trigonometric polynomials and entirefunctions of exponential type. The method is based on the constructionof identities expressing the derivatives of a function itself and of itstrigonometrical conjugate in terms of convolution operators. As a consequence,we reduce the constants in the estimates of the norms of the derivativesin terms of best approximations.

AB - We propose a new method for proving the classical inverse theoremsof the theory of approximation by trigonometric polynomials and entirefunctions of exponential type. The method is based on the constructionof identities expressing the derivatives of a function itself and of itstrigonometrical conjugate in terms of convolution operators. As a consequence,we reduce the constants in the estimates of the norms of the derivativesin terms of best approximations.

KW - 517.5

KW - conjugate function

KW - inverse theorems

KW - sharp constants

UR - http://www.scopus.com/inward/record.url?scp=85131567477&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/a365e7a0-0c76-3494-a392-ca122d6e8bbd/

U2 - 10.1134/s0037446622030053

DO - 10.1134/s0037446622030053

M3 - Article

AN - SCOPUS:85131567477

VL - 63

SP - 438

EP - 450

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 3

ER -

ID: 101356304