Abstract
We obtain estimates of approximation numbers of integral operators, with the kernels belonging to Sobolev classes or classes of functions with bounded mixed derivatives. Along with the estimates of approximation numbers, we also obtain estimates of best bilinear approximation of such kernels.
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T. Figiel, J. Lindenstrauss, V. D. Milman (1977):The dimension of almost spherical sections of convex bodies. Acta math.,139:53–94.
I. C. Gohberg, M. G. Krein (1969): Introduction to the Theory of Linear Nonselfadjoint Operators. Moscow: Nauka. English transl., 1969, Providence, RI: American Mathematical Society.
S. Heinrich (1985):On the optimal error of degenerate kernel methods. J. Integral Equations,9:251–266.
H. König (1986): Eigenvalue Distribution of Compact Operators. Basel: Birkhäuser.
A. Pietsch (1987): Eigenvalues ands-Numbers. Leipzig: Academische Verlagsgesellschaft. Cambridge: Cambridge University Press.
V. N. Temlyakov (1986):On best bilinear approximations of periodic functions of several variables. Soviet Math. Dokl.,33(1):96–99.
V. N. Temlyakov (1986):Pribligenie periodicheskih mnogih peremennyh kombinaciyami funkcii, zavisyaschih ot men'shego chisla peremennyh. Trudy MIAN,173:243–252. English transl. Proc. Steklov Inst. Math., 1987, No. 4 (173).
V. N. Temlyakov (1986):Approximation of functions with bounded mixed derivative. Trudy Mat. Inst. Steklov,178. English transl. Proc. Steklov Inst. Math., 1989, No. 1 (178).
V. N. Temlyakov (1987):On widths of function classes Soviet Math. Dokl.,35(3):639–642.
V. N. Temlyakov (1987):Estimates of the best bilinear approximations of functions of two variables and some of their applications. Mat. Sb.134(176), No. 1, 93–107. English transl. Math. USSR-Sb.,62, 1989, No. 1, 95–109.
V. N. Temlyakov (1988):Bilinear approximation and connected questions. In: Constructive Theory of Functions '87. Sofia: Bulgarian Academy of Sciences, pp. 448–454.
V. N. Temlyakov (1989):Bilineinay approximatiy i prilogeniy. Trudy MIAN187: 191–215.
V. N. Temlyakov (1989):Ocenki asimptoticheskih harakteristik klassov funkcii s ogranichennoi smeshannoi proizvodnoi ili raznost'ju. Trudy MIAN,189:138–168.
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Communicated by Charles A. Micchelli.
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Temlyakov, V.N. On estimates of approximation numbers and best bilinear approximation. Constr. Approx 8, 23–33 (1992). https://doi.org/10.1007/BF01208903
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DOI: https://doi.org/10.1007/BF01208903