Unique minimality of Fourier projections
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- by S. D. Fisher, P. D. Morris and D. E. Wulbert PDF
- Trans. Amer. Math. Soc. 265 (1981), 235-246 Request permission
Abstract:
The question of when the Fourier projection is the only one of least norm from a space of continuous functions on the circle onto spaces spanned by trigonometric polynomials is studied in two settings. In the first the domain space is the disc algebra and the range is finite-dimensional. In the second the domain space consists of all real continuous functions and the range has finite codimension.References
- D. L. Berman, On the impossibility of constructing a linear polynomial operator furnishing an approximation of the order of the best approximation, Dokl. Akad. Nauk SSSR 120 (1958), 1175–1177 (Russian). MR 0098941
- E. W. Cheney, Introduction to approximation theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0222517
- E. W. Cheney, C. R. Hobby, P. D. Morris, F. Schurer, and D. E. Wulbert, On the minimal property of the Fourier projection, Trans. Amer. Math. Soc. 143 (1969), 249–258. MR 256044, DOI 10.1090/S0002-9947-1969-0256044-3
- Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655 F. R. Gantmacher, The theory of matrices, Vol. II, Chelsea, New York, 1959.
- Pol V. Lambert, Minimum norm property of the Fourier projection in spaces of continuous functions, Bull. Soc. Math. Belg. 21 (1969), 359–369. MR 273292
- Pol V. Lambert, On the minimum norm property of the Fourier projection in $L^{1}$-spaces, Bull. Soc. Math. Belg. 21 (1969), 370–391. MR 273293 S. M. Lozinski, On a class of linear operators, Dokl. Akad. Nauk SSSR 61 (1948), 193-196. J. Marcinkiewicz, Quelques remarques sur l’interpolation, Acta Litt. Sci. (Szeged) 8 (1937), 127-130.
- Morris Marden, Geometry of polynomials, 2nd ed., Mathematical Surveys, No. 3, American Mathematical Society, Providence, R.I., 1966. MR 0225972
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 265 (1981), 235-246
- MSC: Primary 46E15; Secondary 41A35, 42A05
- DOI: https://doi.org/10.1090/S0002-9947-1981-0607118-1
- MathSciNet review: 607118