Limit semigroups of Bernstein-Schnabl operators associated with positive projections
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1989)
- Volume: 16, Issue: 2, page 259-279
- ISSN: 0391-173X
Access Full Article
topHow to cite
topAltomare, Francesco. "Limit semigroups of Bernstein-Schnabl operators associated with positive projections." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 16.2 (1989): 259-279. <http://eudml.org/doc/84054>.
@article{Altomare1989,
author = {Altomare, Francesco},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {compact convex subset of a locally convex Hausdorff space; Banach lattice of all continuous real-valued functions; positive operators; Bernstein- Schnabl operator; infinite lower triangular stochastic matrix; selection of representing measures; Bauer simplex},
language = {eng},
number = {2},
pages = {259-279},
publisher = {Scuola normale superiore},
title = {Limit semigroups of Bernstein-Schnabl operators associated with positive projections},
url = {http://eudml.org/doc/84054},
volume = {16},
year = {1989},
}
TY - JOUR
AU - Altomare, Francesco
TI - Limit semigroups of Bernstein-Schnabl operators associated with positive projections
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1989
PB - Scuola normale superiore
VL - 16
IS - 2
SP - 259
EP - 279
LA - eng
KW - compact convex subset of a locally convex Hausdorff space; Banach lattice of all continuous real-valued functions; positive operators; Bernstein- Schnabl operator; infinite lower triangular stochastic matrix; selection of representing measures; Bauer simplex
UR - http://eudml.org/doc/84054
ER -
References
top- [1] F. Altomare, Proiettori positivi, famiglie risolventi e problema di Dirichlet, Ricerche Mat., Vol. XXVI (1977), 1, 63-78. Zbl0368.46029MR626371
- [2] F. Altomare, Operatori di Lion sul prodotto di spazi compatti, semigruppi di operatori positivi e problemi di Dirichlet, Ricerche Mat., Vol. XXVIII (1978), 1, 33-58. Zbl0389.46013MR524683
- [3] F. Altomare, Teoremi di approssimazione di tipo Korovkin in spazi di funzioni, Rend. Mat., (6), 13 (1980), no. 3, 409-429. Zbl0455.41010MR609483
- [4] D.H. Armitage, A linear function from a space of polynomials onto a space of harmonic polynomials, J. London Math. Soc. (2), 5 (1972), 529-538. Zbl0244.31007MR315152
- [5] H. Bauer, Theorems of Korovkin type for adapted spaces, Ann. Inst. Fourier (Grenoble) 23 (1973), 245-260. Zbl0262.31005MR358178
- [6] H. Berens - G.G. Lorentz, Geometric theory of Korovkin sets, J. Approx. Theory15 (1975), 161-189. Zbl0322.41018MR390599
- [7] M. Brelot - G. Choquet, Polynômes harmoniques et polyharmoniques, Second Colloque sur les équations aux dérivées partielles (Bruxelles, 1954). Zbl0066.31802MR69968
- [8] M.R. Da Silva, Nonnegative order iterates of Bernstein polynomials and their limiting semigroups, Portugal Math.42 (1983-84), no. 3, 225-248 (1985). Zbl0562.41007MR819903
- [9] G. Felbecker - W. Schempp, A generalization of Bohman-Korovkin's theorem, Math. Z.122 (1971) 63-70. Zbl0203.13004MR291698
- [10] J.A. Goldstein, Semigroups of linear operators and applications, Oxford University Press, New York, 1985. Zbl0592.47034MR790497
- [11] M.W. Grossman, Note on a generalized Bohman-Korovkin theorem, J. Math. Anal. Appl.45 (1974), 43-46. Zbl0269.41019MR336171
- [12] S. Karlin - Z. Ziegler, Iteration of positive approximation operators, J. Approx. Theory3 (1970), 310-339. Zbl0199.44702MR277982
- [13] R.P. Keliski - T.J. Rivlin, Iterates of Bernstein polynomials, Pacific J. Math.21 (1967), no. 3, 511-520. Zbl0177.31302MR212457
- [14] C.A. Micchelli, The saturation class and iterates of the Bernstein polynomials, J. Approx. Theory, 8 (1973), 1-18. Zbl0258.41012MR344757
- [15] J. Nagel, Asymptotic properties of powers of Bernstein operators, J. Approx. Theory, 29 (1980) 323-335. Zbl0454.41016MR598726
- [16] R. Nageled., One-parameter semigroups of positive operators, Lecture Notes in Mathematics, n. 1184, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1986. Zbl0585.47030MR839450
- [17] T. Nishishiraho, A generalization of the Bernstein polynomials and limit of its iterations, Sci. Rep. Kanazawa Univ., 19 (1974), no. 1, 1-7. Zbl0305.41012MR358189
- [18] T. Nishishiraho, Saturation of positive linear operators, Tôhoku Math. J.28 (1976), 239-243. Zbl0327.41018MR415153
- [19] T. Nishishiraho, The degree of convergence of positive linear operators, Tôhoku Math. J.29 (1977), 81-89. Zbl0345.41011MR438003
- [20] T. Nishishiraho, Saturation of bounded linear operators, Tôhoku Math. J.30 (1978), 69-81. Zbl0379.41013MR493510
- [21] T. Nishishiraho, Convergence of positive linear approximation processes, Tôhoku Math. J. (2) 35 (1983) n. 3, 441-458. Zbl0525.41019MR711359
- [22] T. Nishishiraho, The convergence and saturation of iterations of positive linear operators, Math. Z.194, 397-404 (1987). Zbl0596.41036MR879940
- [23] W. Schempp, A note on Korovkin test families, Arch. Math.23 (1972) 521-524. Zbl0229.41013MR318854
- [24] R. Schnabl, Eine Verallgemeinerung der Bernsteinpolynome, Math. Ann.179 (1968), 74-82. Zbl0165.38401MR236586
- [25] R. Schnabl, Zum Saturationsproblem der Verallgemeinerten Bernsteinoperatoren, Proc. Conf. on "Abstract spaces and approximation" held at Oberwolfach, July 18-27, 1968, edited by P.L. Butzer and B.Sz.-Nagy, BirkhäuserBasel, 1969, 281-289. Zbl0186.37901MR271610
- [26] R. Schnabl, Über Gleichmäßige Approximation durch Positive Lineare Operatoren, Constructive theory of functions (Proc. Internat. Conf. Vama, 1970) 287-296, Izdat. Bolgar. Akad. Nauk Sofia, 1972. Zbl0239.46054MR370012
- [27] P.C. Sikkema, Über Potenzen von Verallgemeinerten Bernstein Operatoren, Mathematica (Cluj) 8-31, 1 (1966), 173-180. Zbl0166.31801MR209735
- [28] H.F. Trotter, Approximation of semi-groups of operators, Pacific J. Math.8 (1958), 887-919. Zbl0099.10302MR103420
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.