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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Interpolation of Besov spaces
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by Ronald A. DeVore and Vasil A. Popov PDF
Trans. Amer. Math. Soc. 305 (1988), 397-414 Request permission

Abstract:

We investigate Besov spaces and their connection with dyadic spline approximation in ${L_p}(\Omega )$, $0 < p \leqslant \infty$. Our main results are: the determination of the interpolation spaces between a pair of Besov spaces; an atomic decomposition for functions in a Besov space; the characterization of the class of functions which have certain prescribed degree of approximation by dyadic splines.
References
  • Carl de Boor, The quasi-interpolant as a tool in elementary polynomial spline theory, Approximation theory (Proc. Internat. Sympos., Univ. Texas, Austin, Tex., 1973) Academic Press, New York, 1973, pp. 269–276. MR 0336159
  • C. de Boor and G. J. Fix, Spline approximation by quasiinterpolants, J. Approximation Theory 8 (1973), 19–45. MR 340893, DOI 10.1016/0021-9045(73)90029-4
  • Yu. Brudnyi, Approximation of functions of $n$-variables by quasi-polynomials, Math. USSR Izv. 4 (1970), 568-586.
  • Paul L. Butzer and Hubert Berens, Semi-groups of operators and approximation, Die Grundlehren der mathematischen Wissenschaften, Band 145, Springer-Verlag New York, Inc., New York, 1967. MR 0230022
  • Z. Ciesielski, Constructive function theory and spline systems, Studia Math. 53 (1975), no. 3, 277–302. MR 417630, DOI 10.4064/sm-53-3-277-302
  • Ronald A. DeVore, Degree of approximation, Approximation theory, II (Proc. Internat. Sympos., Univ. Texas, Austin, Tex., 1976) Academic Press, New York, 1976, pp. 117–161. MR 0440865
  • R. DeVore and V. Popov, Interpolation and non-linear approximation, Proc. Conf. on Interpolation and Allied Topics in Analysis, Lund, 1986 (to appear).
  • Ronald A. DeVore and Vasil A. Popov, Free multivariate splines, Constr. Approx. 3 (1987), no. 2, 239–248. MR 889558, DOI 10.1007/BF01890567
  • R. Devore and K. Scherer, A constructive theory for approximation by splines with an arbitrary sequence of knot sets, Approximation theory (Proc. Internat. Colloq., Inst. Angew. Math., Univ. Bonn, Bonn, 1976) Springer, Berlin, 1976, pp. 167–183. MR 0614156
  • Ronald A. DeVore and Robert C. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc. 47 (1984), no. 293, viii+115. MR 727820, DOI 10.1090/memo/0293
  • Michael Frazier and Björn Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), no. 4, 777–799. MR 808825, DOI 10.1512/iumj.1985.34.34041
  • Jaak Peetre, New thoughts on Besov spaces, Duke University Mathematics Series, No. 1, Duke University, Mathematics Department, Durham, N.C., 1976. MR 0461123
  • Pencho P. Petrushev, Direct and converse theorems for spline and rational approximation and Besov spaces, Function spaces and applications (Lund, 1986) Lecture Notes in Math., vol. 1302, Springer, Berlin, 1988, pp. 363–377. MR 942281, DOI 10.1007/BFb0078887
  • E. A. Storozhenko and P. Oswald, Jackson’s theorem in the spaces ${L_p}({{\mathbf {R}}^k})$, $0 < p < 1$, Siberian Math. J. 19 (1978), 630-639. V. A. Popov and P. Petrushev, Rational approximation of real valued functions, Encyclopedia of Math, and Applications, vol. 28, Cambridge Univ. Press, Cambridge, 1987.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 305 (1988), 397-414
  • MSC: Primary 46E35; Secondary 41A15, 46M35
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0920166-3
  • MathSciNet review: 920166