Geodesic
Sampling Numbers and Embedding Constants
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 275-284.

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The paper deals with the spaces $G_1(\Omega)=A^s_{pq}(\Omega)$ of Sobolev–Besov type in bounded Lipschitz domains $\Omega$ in $\mathbb R^n$ such that $G_1(\Omega)$ is compactly embedded in $C(\overline{\Omega})$. Sampling numbers measure the accuracy of the recovery of $f \in G_1(\Omega)$ in diverse target spaces $G_2(\Omega)$ of the same type. We prove equivalence assertions for these numbers and study what happens in limiting situations. 
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H. Triebel. Sampling Numbers and Embedding Constants. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 275-284. http://geodesic.mathdoc.fr/item/TM_2005_248_a24/

[1] Besov O.V., Ilin V.P., Nikolskii S.M., Integralnye predstavleniya funktsii i teoremy vlozheniya, 2-e izd., Nauka, M., 1996 | MR

[2] DeVore R.A., Sharpley R.C., “Besov spaces on domains in $\mathbb R^d$”, Trans. Amer. Math. Soc., 335 (1993), 843–864 | DOI | MR | Zbl

[3] Kudryavtsev S.N., “Nekotorye zadachi teorii priblizhenii dlya odnogo klassa funktsii konechnoi gladkosti”, Mat. sb., 183:2 (1992), 3–20

[4] Kudryavtsev S.N., “Vosstanovlenie funktsii vmeste s ikh proizvodnymi po znacheniyam funktsii v zadannom chisle tochek”, Izv. RAN. Ser. mat., 58:6 (1994), 79–104 | MR | Zbl

[5] Kudryavtsev S.N., “Nailuchshaya tochnost vosstanovleniya funktsii konechnoi gladkosti po ikh znacheniyam v zadannom chisle tochek”, Izv. RAN. Ser. matem., 62:1 (1998), 21–58 | MR | Zbl

[6] Narcowich F.J., Ward J.D., Wendland H., “Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting”, Math. Comput., 74 (2005), 743–763 | DOI | MR | Zbl

[7] Nikolskii S.M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, 2-e izd., Nauka, M., 1977 | MR

[8] Novak E., Triebel H., Function spaces on Lipschitz domains and optimal rates of convergence for sampling, Preprint, Jena, 2004

[9] Traub J.F., Wasilkowski G.W., Woźniakowski H., Information-based complexity, Acad. Press, Boston, 1988 | MR | Zbl

[10] Triebel H., Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam, 1978 ; 2nd ed., Barth, Heidelberg, 1995 ; Трибель Х., Теория интерполяции, функциональные пространства, дифференциальные операторы, Мир, М., 1980 | MR | Zbl | Zbl | MR

[11] Triebel H., Theory of function spaces, Birkhäuser, Basel, 1983 ; Трибель Х., Теория функциональных пространств, Мир, М., 1986 | MR | Zbl | MR | Zbl

[12] Triebel H., Theory of function spaces. II, Birkhäuser, Basel, 1992 | MR | Zbl

[13] Triebel H., Fractals and spectra, Birkhäuser, Basel, 1997 | MR | Zbl

[14] Triebel H., The structure of functions, Birkhäuser, Basel, 2001 | MR | Zbl

[15] Triebel H., “Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers”, Rev. Mat. Complut., 15 (2002), 475–524 | MR | Zbl

[16] Triebel H., “A note on wavelet bases in function spaces”, Orlicz centenary volume, Banach Center Publ., 64, Pol. Acad. Sci., Warsaw, 2004, 193–206 | MR | Zbl