Geodesic
Korovkin Theorems for Integral Operators with Kernels of Finite Oscillation
Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1390-1404

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

There has been considerable interest recently in the investigation of "Korovkin sets". Briefly, for X a Banach space and a family of linear operators on X, a subset K ⊂ X is a Korovkin set relative to if for any bounded sequence {Tn } ⊂ , Tnk → k in X for each k ∊ K implies Tnx → x for each x ∊ X. A large portion of these investigations have been carried out for X being one of the spaces C(S), S compact Hausdorff, the usual Lp spaces of functions on some finite measure space, or some Banach lattice; while is one of the classes +-positive operators, 1-contractions (i.e., ||T||1), or + ⋂ 1 
Marsden, M. J.; Riemenschneider, S. D. Korovkin Theorems for Integral Operators with Kernels of Finite Oscillation. Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1390-1404. doi: 10.4153/CJM-1974-133-4
@article{10_4153_CJM_1974_133_4,
     author = {Marsden, M. J. and Riemenschneider, S. D.},
     title = {Korovkin {Theorems} for {Integral} {Operators} with {Kernels} of {Finite} {Oscillation}},
     journal = {Canadian journal of mathematics},
     pages = {1390--1404},
     year = {1974},
     volume = {26},
     number = {6},
     doi = {10.4153/CJM-1974-133-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-133-4/}
}
TY  - JOUR
AU  - Marsden, M. J.
AU  - Riemenschneider, S. D.
TI  - Korovkin Theorems for Integral Operators with Kernels of Finite Oscillation
JO  - Canadian journal of mathematics
PY  - 1974
SP  - 1390
EP  - 1404
VL  - 26
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-133-4/
DO  - 10.4153/CJM-1974-133-4
ID  - 10_4153_CJM_1974_133_4
ER  - 
%0 Journal Article
%A Marsden, M. J.
%A Riemenschneider, S. D.
%T Korovkin Theorems for Integral Operators with Kernels of Finite Oscillation
%J Canadian journal of mathematics
%D 1974
%P 1390-1404
%V 26
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-133-4/
%R 10.4153/CJM-1974-133-4
%F 10_4153_CJM_1974_133_4

[1] 1. Achieser, N. I., Vorlesungen über Approximationstheorie (Akademie-Verlag, Berlin, 1967). Google Scholar

[2] 2. Butzer, P. L., A survey of work on approximation at Aachen, 1968-1972. In “Approximation Theory, pp. 31-100, Proc. 1973 Austin Conf. G. G. Lorentz ed. (Academic Press, New York, 1973). Google Scholar

[3] 3. Butzer, P. L., Nessel, R. J., and K. Scherer, Trigonometric convolution operators with kernels having alternating signs and their degree of convergence, Jber. Deutsch. Math.-Verein 70 (1967), 86–99. Google Scholar

[4] 4. DeVore, R. and Richards, F., The degree of approximation by Chebyshevian Splines, Trans. Amer. Math. Soc. 181 (1973), 401–418. Google Scholar

[5] 5. Ditzian, Zeev and Freud, Geza, Linear approximating processes with limited oscillation (to appear in J. Approximation Theory). Google Scholar

[6] 6. Dzjadyk, V. K., Approximation of functions by positive linear operators and singular integrals (Russian), Mat. Sb. 70 (1966), 508–517. Google Scholar

[7] 7. Karlin, S. and Studden, W. J., Tchebycheff systems: with applications in analysis and statistics (Interscience Publishers, New York, 1966). Google Scholar

[8] 8. Korovkin, P. P., Convergent sequences of linear operators (Russian), Uspehi Mat. Nauk 17 (1962), 147–152. Google Scholar

[9] 9. Korovkin, P. P., On the order of approximation of functions by linear polynomial operators of the class , In “Studies of Contemporary Problems in the Constructive Theory of Functions“ (Proc. Second All-Union Conf. on the Constructive theory of Functions, Baku 1962), I. I. Ibragimov Editor, Acad. Sci. Azerbaijani SSR Inst. Math. Mech., Izad. Akad. Nauk Azerbaidžan SSR, Baku, 1965, 163-166. Google Scholar

[10] 10. Shapiro, H. S., Topics in approximation theory (Springer-Verlag, Berlin, 1971). Google Scholar

[11] 11. Willett, D., Disconjugacy tests for singular linear differential equations, SIAM J. Math. Anal. 2 (1971), 536–545. Google Scholar

Cité par Sources :