Counter-examples to Markov and Bernstein inequalities
✍ Scribed by P Goetgheluck; W Pleśniak
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 335 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0021-9045
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📜 SIMILAR VOLUMES
An infinite Markov system \(\left\{f_{0}, f_{1}, \ldots\right\}\) of \(C^{2}\) functions on \([a, b]\) has dense span in \(C[a, b]\) if and only if there is an unbounded Bernstein inequality on every subinterval of \([a, b]\). That is if and only if, for each \([\alpha, \beta]=[a, b], \alpha \neq \b
The principal result of this paper is the following Markov-type inequality for Mu ntz polynomials. Theorem (Newman's Inequality in L p [a, b] for [a, b]/(0, )). Let 4 := (\\* j ) j=0 be an increasing sequence of nonnegative real numbers. Suppose \\* 0 =0 and there exists a $>0 so that \\* j $j for e