Geodesic
Interpolation by Polynomials in z and z –1 in the Roots of Unity
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 16-23

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

Given a function ƒ(z), continuous on C: |z| = 1 in the complex plane, there is a close analogy between approximation in the sense of least squares by polynomials on the unit circle and interpolation by polynomials in the nth roots of unity to the same function. For detailed discussion of the problem and its generalization for a suitable Jordan curve one can refer to Walsh (3) or to a recent paper by Curtiss (2). More recently, Curtiss (1) has considered the problem of interpolation by polynomials in non-equally spaced points on the unit circle and has pointed out the limitations inherent in the problem. 
Sharma, A. Interpolation by Polynomials in z and z –1 in the Roots of Unity. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 16-23. doi: 10.4153/CJM-1967-002-6
@article{10_4153_CJM_1967_002_6,
     author = {Sharma, A.},
     title = {Interpolation by {Polynomials} in z and z {\textendash}1 in the {Roots} of {Unity}},
     journal = {Canadian journal of mathematics},
     pages = {16--23},
     year = {1967},
     volume = {19},
     number = {1},
     doi = {10.4153/CJM-1967-002-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-002-6/}
}
TY  - JOUR
AU  - Sharma, A.
TI  - Interpolation by Polynomials in z and z –1 in the Roots of Unity
JO  - Canadian journal of mathematics
PY  - 1967
SP  - 16
EP  - 23
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-002-6/
DO  - 10.4153/CJM-1967-002-6
ID  - 10_4153_CJM_1967_002_6
ER  - 
%0 Journal Article
%A Sharma, A.
%T Interpolation by Polynomials in z and z –1 in the Roots of Unity
%J Canadian journal of mathematics
%D 1967
%P 16-23
%V 19
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-002-6/
%R 10.4153/CJM-1967-002-6
%F 10_4153_CJM_1967_002_6

[1] 1. Curtiss, J. H., Polynomial interpolation in points equidistributed on the unit circle, Pacific J. Math., 12 (1962), 863–877. Google Scholar

[2] 2. Curtiss, J. H., A stochastic treatment of some classical interpolation problems, Proc. Fourth Berkeley Symposium Math. Statistics and Probability, Vol. II (Berkeley, 1961), pp. 79–93. Google Scholar

[3] 3. Walsh, J. L., Interpolation and approximation by rational functions in the complex domain (Providence, 1960). pp. 153–156, 179-182. Google Scholar

[4] 4. Walsh, J. L., Interpolation and an analogue of the Laurent development, Proc. Nat. Acad. Sci., 19 (1) (1933), 203-20. Google Scholar

[5] 5. Walsh, J. L. and Sharma, A.. Least square approximation and interpolation in the roots of unity, Pacific J. Math., 14 (1964), 727–730. Google Scholar

Cité par Sources :