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Solution of the Bernstein Problem in the Non-regular Case

✍ Scribed by J.Carlos Gutiérrez Fernández

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
186 KB
Volume
223
Category
Article
ISSN
0021-8693

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✦ Synopsis

This paper describes explicitly all non-regular non-degenerate simplicial stochas-Ž tic Bernstein algebras. Consequently, the Bernstein problem S. N. Bernstein, Ž . . Science Ukraine 1 1992 , 14᎐19 in the non-degenerate case is settled, since the regular and exceptional cases have already been examined by Y. Lyubich in the 1970s. Notice that from this result it is possible to explicitly describe every Ž . Ž² Ž 2 .: non-regular simplicial algebra A, ⌬ since the simplicial subalgebra supp A , w Ž 2 .x. supp A is non-degenerate. Also we prove the relevant Lyubich's conjecture Ž . 1992, Yu I. Lyubich, Biomathematics 22, 232 in an affirmative way: all normal simplicial stochastic Bernstein algebras are regular.

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