Research output: Contribution to journal › Article › peer-review
Sharp Estimates for Mean Square Approximations of Classes of Differentiable Periodic Functions by Shift Spaces. / Vinogradov, O. L.; Ulitskaya, A. Yu.
In: Vestnik St. Petersburg University: Mathematics, Vol. 51, No. 1, 01.01.2018, p. 15-22.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Sharp Estimates for Mean Square Approximations of Classes of Differentiable Periodic Functions by Shift Spaces
AU - Vinogradov, O. L.
AU - Ulitskaya, A. Yu
PY - 2018/1/1
Y1 - 2018/1/1
N2 - Let L2 be the space of 2π-periodic square-summable functions and E(f, X)2 be the best approximation of f by the space X in L2. For n ∈ ℕ and B ∈ L2, let SB , n be the space of functions s of the form s(x)=∑j=02n−1βjB(x−jπn). This paper describes all spaces SB , n that satisfy the exact inequality E(f,SB,n)2≤1nr∥f(r)∥2. (2n–1)-dimensional subspaces fulfilling the same estimate are specified. Well-known inequalities are for approximation by trigonometric polynomials and splines obtained as special cases.
AB - Let L2 be the space of 2π-periodic square-summable functions and E(f, X)2 be the best approximation of f by the space X in L2. For n ∈ ℕ and B ∈ L2, let SB , n be the space of functions s of the form s(x)=∑j=02n−1βjB(x−jπn). This paper describes all spaces SB , n that satisfy the exact inequality E(f,SB,n)2≤1nr∥f(r)∥2. (2n–1)-dimensional subspaces fulfilling the same estimate are specified. Well-known inequalities are for approximation by trigonometric polynomials and splines obtained as special cases.
KW - best approximation
KW - sharp constants
KW - shift spaces
UR - http://www.scopus.com/inward/record.url?scp=85045068984&partnerID=8YFLogxK
U2 - 10.3103/S1063454118010120
DO - 10.3103/S1063454118010120
M3 - Article
AN - SCOPUS:85045068984
VL - 51
SP - 15
EP - 22
JO - Vestnik St. Petersburg University: Mathematics
JF - Vestnik St. Petersburg University: Mathematics
SN - 1063-4541
IS - 1
ER -
ID: 37832541