Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T04:52:54.694Z Has data issue: false hasContentIssue false

An Application of a Theorem of J. Czipszer and G. Freud to a Problem of Simultaneous Approximation

Published online by Cambridge University Press:  20 November 2018

A.K. Varma*
Affiliation:
University of Florida, Gainesville Florida
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In an earlier work [12] we considered the case of (0, 2, 3) interpolation by trigonometric polynomials at the points , i = 0, 1,…, n-1. By (0, 2, 3) interpolation we mean the problem of finding a trigonometric polynomial of suitable order whose values, second and third derivatives are prescribed at some given points. An interesting distinction between the (0, 2) interpolation studied by the Hungarian mathematician O.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Balázs, J. and Turan, P., Notes on interpolation II. Acta. Math. Acad. Sci. Hungar. 8 (1957) 201215.Google Scholar
2. Balázs, J. and Turán, P., Notes on interpolation III. Acta. Math. Acad. Sci. Hungar. 9 (1958) 195214.Google Scholar
3. Czipszer, J. and Freud, G., Sur l′approximation d′une fonction périodique et de ses dérivées successives par un polynome trigonométrique et par ses dérivées successives. Acta. Math. 99 (1958) 3351.Google Scholar
4. Davis, P. J., Interpolation and approximation theory. (Blaisdell Pub. Co. 1963.)Google Scholar
5. Freud, G., Über differenzierte folgen der Lagrangechen interpolation. Acta. Math. Sci. Hungar. 7 (1956) 467473.Google Scholar
6. Garkavi, A. L., Simultaneous approximation to a periodic function and its derivatives by means of trigonometric polynomials. Izv. Akad. Nauk. SSSR. Ser. Mat. 24 (1960) 103128. (Russian).Google Scholar
7. Jackson, D., Theory of approximation. (Amer. Math. Soc. Colloq. Pub. No. 11.)Google Scholar
8. Kiš, O., On trigonometric interpolation. Acta. Math. Acad. Sci. Hungar. 11 (1960) 256276. (Russian).Google Scholar
9. Timan, A.F., Simultaneous approximation of functions and their derivatives on the whole realax is. Izv. Akad. Nauk. SSSR. Ser. Mat. 24 (1960) 420430; English translation Amer. Math. Soc. Translation series 2, 44, 111.Google Scholar
10. Varma, A.K., On a problem of P. Turán on Lacunary interpolation. Canad. Math. Bull. 10 (1967) 531557.Google Scholar
11. Varma, A.K. and Sharma, A., Trigonometric interpolation. Duke Math. J. 32 (1965) 341358.Google Scholar
12. Varma, A.K., Trigonometric interpolation II. Annales Polonici Math. (Poland) 21 (1968) 5158; same version in E. L. Whitney Memorial Volume, University of Alberta, Edmonton.Google Scholar
13. Varma, A.K., Simultaneous approximation of periodic continuous functions and their derivatives. Israel J. Math. Vol. 6, No. 1 (1968) 6673.Google Scholar