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Abstrakty
In the paper, the behavior of Fourier coefficients of some classes of functions on an arbitrary orthogonal system is studied. The estimates of order of convergence to zero of Fourier-Gegenbauer coefficients are found. These estimates are precise and are of terminal character. The obtained results are used in convergence of Fourier-Gegenbauer series.
Wydawca
Czasopismo
Rocznik
Tom
Strony
209--246
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
- Azerbaijan State Oil Academy 20, Azadliq Ave., Baku, Az1010, Azerbaijan
Bibliografia
- [1] Ar.S. Jafarov On Fourier-Legandre coefficients. Dokl. An. Azerb. SSR, vol. No XXXV, 9 (1979), 3-7.
- [2] M.Sh. Jamalaov On estimation of Fourier coefficients by ultraspherical polynomials . Dep. in. VINIITI, No 4419-81 (1982).
- [3] I.S.Gradshteyn, I.I. Rizhik, Table of Integrals Summs, Series and Product, M.1971
- [4] O.H.Hardy, I.E.Littlwood, G.Polya, Inequalities, M. 1948.
- [5] I.P. Natanson Theory of functions of real variable. Costechizdat, 1957.
- [6] M.K.Potapov, On approximation of functions by Jacobi polynomials, Vestn. Moskov. Univ. Mathem. 5 (1977), 70-82.
- [7] S.Z.Rafalson, On approximation of the functions of Fourier-Jacobi sums, Izvestiya vuzov, Mathem. 4 (1968), 54-62
- [8] R.L.Stens, M.Wehrens, Legendre transform method and best algebraic approximation, Rocz. Pol. Tow. Mat. XXI (1979), 351-380.
- [9] G. Sege Orthogonal polynomials. Fizmatgiz, M. 1962
- [10] M. Wehrens Best approximation on the unit sphere in Rk. Functional Analysis and Approximation (1980), 233-245.
- [11] A. Zigmund Trigonometric series. vol.1, mir. M. 1965.
- [12] A.V. Zorshikov On estimations of Fourier-Jacobi residuals. Matem. zapiski Ukr.Gos. Univ, vol. V(4), (1966), 23-32.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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