Geodesic
Optimal subspaces for mean square approximation of classes of differentiable functions on the half-line
Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part III, Tome 539 (2024), pp. 44-65 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We obtain sharp inequalities for the best mean square approximation of two classes of functions on the half-line, defined by boundary conditions corresponding to even and odd extension of a function. Optimal subspaces are provided by even and odd parts of the spaces generated by equidistant shifts of a single function. Under certain additional conditions on this function, the sharpness of the inequalities in the sense of average widths is proved. 
@article{ZNSL_2024_539_a2,
     author = {O. L. Vinogradov and A. Yu. Ulitskaya},
     title = {Optimal subspaces for mean square approximation of classes of differentiable functions on the half-line},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {44--65},
     year = {2024},
     volume = {539},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_539_a2/}
}
TY  - JOUR
AU  - O. L. Vinogradov
AU  - A. Yu. Ulitskaya
TI  - Optimal subspaces for mean square approximation of classes of differentiable functions on the half-line
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2024
SP  - 44
EP  - 65
VL  - 539
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2024_539_a2/
LA  - ru
ID  - ZNSL_2024_539_a2
ER  - 
%0 Journal Article
%A O. L. Vinogradov
%A A. Yu. Ulitskaya
%T Optimal subspaces for mean square approximation of classes of differentiable functions on the half-line
%J Zapiski Nauchnykh Seminarov POMI
%D 2024
%P 44-65
%V 539
%U http://geodesic.mathdoc.fr/item/ZNSL_2024_539_a2/
%G ru
%F ZNSL_2024_539_a2
O. L. Vinogradov; A. Yu. Ulitskaya. Optimal subspaces for mean square approximation of classes of differentiable functions on the half-line. Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part III, Tome 539 (2024), pp. 44-65. http://geodesic.mathdoc.fr/item/ZNSL_2024_539_a2/

[1] G. G. Magaril-Ilyaev, “Srednyaya razmernost, poperechniki i optimalnoe vosstanovlenie sobolevskikh klassov funktsii na pryamoi”, Mat. sbornik, 182:11 (1991), 1635–1656

[2] O. L. Vinogradov, A. Yu. Ulitskaya, “Tochnye otsenki srednekvadratichnykh priblizhenii klassov differentsiruemykh periodicheskikh funktsii prostranstvami sdvigov”, Vestnik SPbGU. Matematika. Mekhanika. Astronomiya, 5 (63):1 (2018), 22–31

[3] A. Yu. Ulitskaya, “Tochnye otsenki srednekvadratichnykh priblizhenii klassov svertok prostranstvami sdvigov na osi”, Sib. mat. zh., 64:1 (2023), 184–203 | MR | Zbl

[4] A. Kolmogorov, “Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse”, Ann. Math., 37 (1936), 107–110 | DOI | MR | Zbl

[5] M. S. Floater, E. Sande, “Optimal spline spaces for $L^2$ $n$-width problems with boundary conditions”, Const. Approx., 2018, 1–18 | MR

[6] O. L. Vinogradov, A. Yu. Ulitskaya, “Optimalnye podprostranstva dlya srednekvadratichnykh priblizhenii klassov differentsiruemykh funktsii na otrezke”, Vestnik SPbGU. Matematika. Mekhanika. Astronomiya, 7 (65):3 (2020), 404–417 | MR | Zbl

[7] R.-Q. Jia, C. A. Micchelli, “Using the refinement equations for the construction of pre-wavelets II: powers of two”, Curves and Surfaces, eds. P.-J. Laurent, A. Le Mehaute, L. L. Schumaker, Academic Press, New York, 1991, 209–246 | DOI | MR

[8] A. Ron, “Introduction to shift-invariant spaces. Linear independence”, Multivariate approximation and applications, eds. N. Dyn et.al, Cambridge University Press, Cambridge, 2001, 112–151 | DOI | MR | Zbl

[9] C. de Boor, R. DeVore, A. Ron, “Approximation from shift-invariant subspaces of $L_2(\mathbb{R}^d)$”, Trans. Amer. Math. Soc., 341:2 (1994), 787–806 | MR | Zbl

[10] B. Ya. Levin, Lectures on entire functions, AMS, Providence, Rhode Island, 1996 | MR | Zbl

[11] A. Yu. Ulitskaya, “Fourier analysis in spaces of shifts”, J. Math. Sci., 266:4 (2022), 603–614 | DOI | MR | Zbl

[12] O. L. Vinogradov, “Srednyaya razmernost prostranstv sdvigov i ikh podprostranstv”, Mat. zametki, 116:5 (2024), 694–706 | DOI

[13] N. I. Akhiezer, Lektsii po teorii approksimatsii, Nauka, M., 1965

[14] M. Skopina, A. Krivoshein, V. Protasov, Multivariate wavelet frames, Springer, Singapore, 2016 | MR | Zbl

[15] O. L. Vinogradov, “Average dimension of shift spaces”, Lobachevskii J. Math., 39:5 (2018), 717–721 | DOI | MR | Zbl