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Construction of homogeneous spaces of local functions and inverse approximation theorems

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Abstract

The paper's first part is devoted to the construction of systems, finitary inR n, of functions

for approximations of the form The concepts of ℓ-approximating and

-interpolating systems of functions

are introduced, methods of constructing them are examined, and the labor consumption of the matrices of a variational-difference method is discussed when different systems of functions

are used. The paper's second part contains inverse approximation theorems for metric spaces and their application in the case of approximations by spaces of local functions in Sobolev norms.

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Literature cited

  1. S. G. Mikhlin, “Variational-difference approximation,” J. Sov. Math.,10, No. 5 661–787 (1978).

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  2. G. Strang, “The finite element method and approximation theory,” in: B. Hubbard (ed.), Numerical Solution of Partial Differential Equations. II (SYNSPADE 1970), Academic Press, New York-London (1971), pp. 547–583.

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  3. Yu. K. Dem'yanovich, “Approximation by local functions in a space with fractional derivatives,” Differents. Uravn. Primen. — Tr. Sem. Protsessy Optimal. Upravlen. I Sekts., No. 11, 35–49 (1975).

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  4. Yu. K. Dem'yanovich, “On approximation by spaces of local functions,” Vestn. Leningr. Gos. Univ., No. 1, 35–41 (1977).

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Authors
  1. Yu. K. Dem'yanovich
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 90, pp. 5–23, 1979.

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Dem'yanovich, Y.K. Construction of homogeneous spaces of local functions and inverse approximation theorems. J Math Sci 20, 1897–1912 (1982). https://doi.org/10.1007/BF01680561

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  • DOI: https://doi.org/10.1007/BF01680561

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