Skip to main content
Log in

On estimates of approximation numbers and best bilinear approximation

  • Published:
Constructive Approximation Aims and scope

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. T. Figiel, J. Lindenstrauss, V. D. Milman (1977):The dimension of almost spherical sections of convex bodies. Acta math.,139:53–94.

    Google Scholar 

  2. 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.

    Google Scholar 

  3. S. Heinrich (1985):On the optimal error of degenerate kernel methods. J. Integral Equations,9:251–266.

    Google Scholar 

  4. H. König (1986): Eigenvalue Distribution of Compact Operators. Basel: Birkhäuser.

    Google Scholar 

  5. A. Pietsch (1987): Eigenvalues ands-Numbers. Leipzig: Academische Verlagsgesellschaft. Cambridge: Cambridge University Press.

    Google Scholar 

  6. V. N. Temlyakov (1986):On best bilinear approximations of periodic functions of several variables. Soviet Math. Dokl.,33(1):96–99.

    Google Scholar 

  7. 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).

    Google Scholar 

  8. 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).

  9. V. N. Temlyakov (1987):On widths of function classes Soviet Math. Dokl.,35(3):639–642.

    Google Scholar 

  10. 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.

    Google Scholar 

  11. V. N. Temlyakov (1988):Bilinear approximation and connected questions. In: Constructive Theory of Functions '87. Sofia: Bulgarian Academy of Sciences, pp. 448–454.

    Google Scholar 

  12. V. N. Temlyakov (1989):Bilineinay approximatiy i prilogeniy. Trudy MIAN187: 191–215.

    Google Scholar 

  13. V. N. Temlyakov (1989):Ocenki asimptoticheskih harakteristik klassov funkcii s ogranichennoi smeshannoi proizvodnoi ili raznost'ju. Trudy MIAN,189:138–168.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by Charles A. Micchelli.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Temlyakov, V.N. On estimates of approximation numbers and best bilinear approximation. Constr. Approx 8, 23–33 (1992). https://doi.org/10.1007/BF01208903

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01208903

AMS classification

Key words and phrases

Navigation