Geodesic
Universally optimal approximation of functionals
Applications of Mathematics, Tome 24 (1979) no. 6, pp. 406-420

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A universal optimal in order approximation of a general functional in the space of continuous periodic functions is constructed and its fundamental properties and some generalizations are investigated. As an application the approximation of singular integrals is considered and illustrated by numerical results.
A universal optimal in order approximation of a general functional in the space of continuous periodic functions is constructed and its fundamental properties and some generalizations are investigated. As an application the approximation of singular integrals is considered and illustrated by numerical results.
DOI : 10.21136/AM.1979.103824
Classification : 30E20, 41A10, 41A15, 41A25, 41A30, 41A55, 65D15, 65D32
Keywords: trigonometric interpolation polynomials; Riesz-Fischer theorem; error functional 
Práger, Milan. Universally optimal approximation of functionals. Applications of Mathematics, Tome 24 (1979) no. 6, pp. 406-420. doi: 10.21136/AM.1979.103824
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[1] I. Babuška: Über universal optimale Quadraturformeln. Teil 1., Apl. mat. 13 (1968), 304- 338, Teil 2., Apl. mat. 13 (1968), 388-404. | MR

[2] K. Segeth: On universally optimal quadrature formulae involving values of derivatives of integrand. Czech. Math. J. 19 (94) 1969, 605-675. | MR | Zbl

[3] S. L. Sobolev: Introduction into the theory of cubature formulae. Nauka, Moscow 1974 (pp. 808). (Russian.) | MR

[4] I. P. Natanson: The constructive theory of functions. GITTL, Moscow, Leningrad 1949. (Russian.) | MR

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