Interpolation of besov spaces

Transactions of the American Mathematical Society

Volumn 305, Issue 1, 1988, Pages 397-414

  Popov, Vasil A ^a  

^a INSTITUTE OF MATHEMATICS AND INFORMATICS   (Bulgaria)

Author keywords

Besov spaces; Degree of approximation; Dyadic splines; Real interpolation spaces

Indexed keywords

EID: 84966241361     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-1988-0920166-3     Document Type: Article

References (15)

1. C. de Boor, The quasi-interpolant as a tool in elementary polynomial spline theory, Approximation Theory (G. G. Lorentz, ed.), Academic Press, New York, 1973, pp. 269-276.
2. C. de Boor and G. F. Fix, Spline approximation by quasi-interpolants, J. Approx. Theory 8 (1973), 19-45.
3. Yu. Brudnyi, Approximation of functions of n-variables by quasi-polynomials, Math. USSR Izv. 4 (1970), 568-586.
4. P. L. Butzer and H. Berens, Semi-groups of operators and approximation, Springer-Verlag, New York, 1967.
5. Z. Ciesielski, Constructive function theory and spline systems, Studia Math. 52 (1973), 277-302.
6. R. DeVore, Degree of approximation, Approximation Theory, II (G. G. Lorentz, C. K. Chui, L. L. Schumaker, eds.), Academic Press, New York, 1976, pp. 117-162.
7. R. DeVore and V. Popov, Interpolation and non-linear approximation, Proc. Conf. on Interpolation and Allied Topics in Analysis, Lund, 1986 (to appear).
8. R- DeVore and V. A. Popov, Free multivariate splines, Constructive Approximation 3 (1987), 239-248.
9. R. DeVore and K. Scherer, A constructive theory for approximation by splines with an arbitrary sequence of knot sets, Approximation Theory, Lecture Notes in Math., vol. 556, SpringerVerlag, New York, 1976.
10. R. DeVore and R. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc., vol. 47, no. 293, 1984.
11. M. Frazier and B. Jawerth, Decomposition of Besov spaces, preprint.
12. J. Peetre, New thoughts on Besov spaces, Duke Univ. Math. Ser. 1, Durham, N.C., 1976.
13. P. Petrushev, Direct and converse theorems for spline and rational approximation and Besov spaces, Proc. Conf. on Interpolation and Applied Topics in Analysis, Lund, 1986 (to appear).
14. E. A. Storozhenko and P. Oswald, Jackson's theorem in the spaces Lp(Rfc), 0 < p < 1, Siberian Math. J. 19 (1978), 630-639.
15. V. A. Popov and P. Petrushev, Rational approximation of real valued functions, Encyclopedia of Math, and Applications, vol. 28, Cambridge Univ. Press, Cambridge, 1987