(0, 2) – Interpolation of Entire Functions
Canadian journal of mathematics, Tome 38 (1986) no. 5, pp. 1210-1227

Voir la notice de l'article provenant de la source Cambridge University Press

Given a triangular matrix A whose n th row consists of the n points (1.1) Turán et al. ([12], [1], [2], [3]) considered the problem of existence, uniqueness, representation, convergence, etc. of polynomials f 2n – 1 of degree ≧2n – 1 where the values of f 2n – 1 and those of its second derivative are prescribed at the points (1.1), i.e., (1.2) The choice of the points (1.1) is important. They found the zeros (1.3) of the polynomial (1.1) where P n – 1 is the (n − 1) Legendre polynomial with the normalization P n – 1(l) = 1 to be the most convenient.
Gervais, R.; Rahman, Q. I.; Schmeisser, G. (0, 2) – Interpolation of Entire Functions. Canadian journal of mathematics, Tome 38 (1986) no. 5, pp. 1210-1227. doi: 10.4153/CJM-1986-061-2
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[1] 1. Balázs, J. and Turán, P., Notes on interpolation. II. (Explicit formulae), Acta Math. Acad. Sci. Hung. 8 (1957), 201–215. Google Scholar

[2] 2. Balázs, J. and Turán, P., Notes on interpolation. III. (Convergence), Acta Math. Acad. Sci. Hung. 9 (1958), 195–214. Google Scholar

[3] 3. Balázs, J. and Turán, P., Notes on interpolation. IV. (Inequalities), Acta Math. Acad. Sci. Hung. 9 (1958), 243–258. Google Scholar

[4] 4. Boas, R. P. Jr., Entire functions (Academic Press, New York, 1954). Google Scholar

[5] 5. Gervais, R. and Rahman, Q. I., An extension of Carlson's theorem for entire functions of exponential type, Trans. Amer. Math. Soc. 235 (1978), 387–394. Google Scholar

[6] 6. Gervais, R. and Rahman, Q. I., An extension of Carlson's theorem for entire functions of exponential type. II, J. Math. Anal. Appl. 69 (1979), 585–602. Google Scholar

[7] 7. Gervais, R., Rahman, Q. I. and Schmeisser, G., Simultaneous interpolation and approximation by entire functions of exponential type, Numerische Methoden der Approximations theorie, Band 4, ISNM 42 (Birkhauser-Verlag, Basel, 1978), 145–153. Google Scholar

[8] 8. Gervais, R., Rahman, Q. I. and Schmeisser, G., Simultaneous interpolation and approximation, In Polynomial and spline approximation (D. Reidel Publ. Comp., Dordrecht-Boston, 1979), 203–223. Google Scholar

[9] 9. Gervais, R., Rahman, Q. I. and Schmeisser, G., Approximation by (0, 2)-interpolating entire functions of exponential type, J. Math. Anal. Appl. 82 (1981), 184–199. Google Scholar

[10] 10. Kiš, O., On trigonometric interpolation (Russian), Acta Math. Acad. Sci. Hung. 11 (1960), 255–276. Google Scholar

[11] 11. Sharma, A. and Varma, A. K., Trigonometric interpolation, Duke Math. J. 32 (1965), 341–358. Google Scholar

[12] 12. Surányi, J. and Turän, P., Notes on interpolation. I. (On some interpolatorical properties of the ultraspherical polynomials), Acta Math. Acad. Sci. Hung. 6 (1955), 67–79. Google Scholar

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