zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Relative infinite-dimensional width of Sobolev classes. (English) Zbl 1205.46018
Summary: In order to consider the problems of relative width of Sobolev classes W p r on in L p , we propose the definition of relative infinite-dimensional width which combines the ideas of the relative width and the infinite-dimensional width. We determine the exact values of relative infinite-dimensional width for r=1, p=1 or p= and for r, p=2.
MSC:
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
41A46Approximation by arbitrary nonlinear expressions; widths and entropy
References:
[1]Konovalov, V. N.: Estimates of diameters of Kolmogorov type for classes of differentiable periodic functions, Mat. zametki 35, No. 3, 369-380 (1984) · Zbl 0561.41022
[2]Konovalov, V. N.: Approximation of Sobolev classes by their sections of finite dimensional, Ukrainian math. J. 54, No. 5, 795-805 (2002) · Zbl 1003.41017 · doi:10.1023/A:1021635530578
[3]Konovalov, V. N.: Approximation of Sobolev classes by their finite-dimensional sections, Math. notes 72, No. 3, 337-349 (2002) · Zbl 1019.41019 · doi:10.1023/A:1020547320561
[4]Subbotin, Yu.N.; Telyakovskii, S. A.: Exact values of relative widths of classes of differentiable functions, Math. notes 65, No. 6, 731-738 (1999) · Zbl 0967.42001 · doi:10.1007/BF02675588
[5]Subbotin, Yu.N.; Telyakovskii, S. A.: Relative widths of classes of differentiable functions in the L2 metric, Uspekhi mat. Nauk 56, No. 4, 159-160 (2001) · Zbl 1036.41013 · doi:10.1070/RM2001v056n04ABEH000432
[6]Subbotin, Yu.N.; Telyakovskii, S. A.: On relative widths of classes of differentiable functions, Proc. Steklov inst. Math. 248, 243-254 (2005) · Zbl 1121.41027
[7]Babenko, V. F.: On the relative widths of classes of functions with bounded mixed derivative, East J. Approx. 2, No. 3, 319-330 (1996) · Zbl 0862.41019
[8]Tikhomirov, V. M.: Some remarks on relative diameters, Banach center publ. 22, 471-474 (1989) · Zbl 0701.41036
[9]Tikhomirov, V. M.: Extremal problems and approximation theory, Adv. math. 19, No. 2, 449-451 (1990) · Zbl 0728.41016
[10]Magaril-Il’yaev, G. G.: φ-mean diameters of classes of functions on the line, Russian math. Surveys 45, No. 2, 218-219 (1990) · Zbl 0737.41027 · doi:10.1070/RM1990v045n02ABEH002340
[11]Magaril-Il’yaev, G. G.: Mean dimension, widths, and optimal recovery of Sobolev classes of functions on the line, Math. USSR-sb. 74, No. 2, 381-403 (1993) · Zbl 0798.41015 · doi:10.1070/SM1993v074n02ABEH003352
[12]Liu, Yongping; Yang, Lianhong: Relative width of smooth classes of multivariate periodic functions with restrictions on iterated Laplace derivatives in the L2-metric, Acta math. Sci. ser. B 26, No. 4, 720-728 (2006) · Zbl 1136.41008 · doi:10.1016/S0252-9602(06)60098-2
[13]Liu, Yongping; Yang, Lianhong: Relative widths of smooth functions determined by fractional order derivatives, J. complexity 24, 259-282 (2008) · Zbl 1141.41007 · doi:10.1016/j.jco.2006.12.001
[14]Xu, Guiqiao: The relative n-widths of Sobolev classes with restrictions, J. approx. Theory 157, 19-31 (2009) · Zbl 1165.41006 · doi:10.1016/j.jat.2008.05.003
[15]Li, Chun: Infinite-dimensional widths in the space of function I, Chinese sci. Bull. 35, 1326-1330 (1990) · Zbl 0751.41012
[16]Li, Chun: Infinite-dimensional widths in the space of functions II, J. approx. Theory 69, 15-34 (1992) · Zbl 0776.41019 · doi:10.1016/0021-9045(92)90046-Q
[17]De Boor, C.; Schoenberg, I. J.: Cardinal interpolation and spline functions, VIII, Lecture notes in math. 501, 1-77 (1976) · Zbl 0319.41010
[18]Sun, Yongsheng; Li, Chun: Optimal recovery for W2r(R) in L2(R), Acta math. Sinica (N.S.) 7, No. 4, 309-323 (1991) · Zbl 0770.46017 · doi:10.1007/BF02594888