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- W2067880143 abstract "Let X be an n-dimensional vector space of functions x from R to Rk. Suppose I is a real interval and r1, …, rk are nonnegative integers with r1 + … + rk = n. We investigate conditions on X, I, and (r1,…,rk) which imply that x = 0 is the only element of X whose ith component xi has ri zeros in I, i = 1, …, k. When k = 1 and the elements of X are sufficiently smooth, Pólya [Trans. Amer. Math. Soc., 29 (1922), 312–324] showed that a sufficient condition is that X has a basis which is a Markov system on I. Moreover this condition is necessary if the elements of X are smooth and I is open or closed. This result is generalized to k ⩾ 1. Examples show how this approach provides criteria for incompatibility of certain classes of linear homogeneous boundary value problems for ordinary differential equations." @default.
- W2067880143 created "2016-06-24" @default.
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- W2067880143 date "1989-10-01" @default.
- W2067880143 modified "2023-09-23" @default.
- W2067880143 title "Markov systems of vector-valued functions and disconjugacy" @default.
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- W2067880143 doi "https://doi.org/10.1016/0021-9045(89)90159-7" @default.
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