Hermite-Birkhoff Interpolation in the nth Roots of Unity

1980 ◽  
Vol 259 (2) ◽  
pp. 621 ◽  
Author(s):  
A. S. Cavaretta ◽  
A. Sharma ◽  
R. S. Varga
Keyword(s):  
Roots Of Unity ◽  
Birkhoff Interpolation

scholarly journals Hermite-Birkhoff interpolation in the $n$th roots of unity

1980 ◽  
Vol 259 (2) ◽  
pp. 621-621
Author(s):  
A. S. Cavaretta ◽  
A. Sharma ◽  
R. S. Varga
Keyword(s):  
Roots Of Unity ◽  
Birkhoff Interpolation

scholarly journals Some Birkhoff interpolation problems on the roots of unity

1985 ◽  
Vol 65 ◽  
pp. 1-23 ◽  
Author(s):  
J. Fabrykowski ◽  
A. Sharma ◽  
H. Zassenhaus
Keyword(s):  
Roots Of Unity ◽  
Birkhoff Interpolation ◽  
Interpolation Problems

Birkhoff Interpolation at the nth Roots of Unity: Convergence

1981 ◽  
Vol 33 (2) ◽  
pp. 362-371 ◽  
Author(s):  
S. D. Riemenschneider ◽  
A. Sharma
Keyword(s):  
Convergence Theorem ◽  
Existence And Uniqueness ◽  
Roots Of Unity ◽  
Second Derivative ◽  
Existence And Uniqueness Theorem ◽  
Birkhoff Interpolation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Convergence Results ◽  
Special Cases

The first investigations on this type of problem were carried out by O. Kiš [2]. Kiš considered the problem of interpolating a function and its second derivative at the nth roots of unity (the (0, 2) problem) by 2n – 1 degree polynomials, and the convergence of such approximates. Later, Sharma [8], [9] extended the existence and uniqueness results to (0, m) interpolation, and essentially to (0, m1, m2) interpolation. In the latter case, Sharma established the convergence results for (0, 2, 3), (0, 1, 3) and (0, 1, 4) interpolation as well. Although some further special cases were considered [10] these were the essential results until very recently. Now Cavaretta, Sharma and Varga [1] have established the existence and uniqueness theorem for all possible interpolations of this type (see Theorem 2.1 below). Motivated by the work of Cavaretta, Sharma and Varga and the earlier work of Sharma [9], a different proof of this result is provided, and this proof is used to establish a convergence theorem in the general case.

scholarly journals Hermite-Birkhoff interpolation on roots of unity and walsh equiconvergence

1983 ◽  
Vol 52-53 ◽  
pp. 603-615 ◽  
Author(s):  
R.B. Saxena ◽  
A. Sharma ◽  
Z. Ziegler
Keyword(s):  
Roots Of Unity ◽  
Birkhoff Interpolation
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