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| Name: | ||||||||||||||||||||
| Miloslav Znojil | ||||||||||||||||||||
| Reviewer number: | ||||||||||||||||||||
| 9689 | ||||||||||||||||||||
| Email: | ||||||||||||||||||||
| znojil@ujf.cas.cz | ||||||||||||||||||||
| Item's zbl-Number: | ||||||||||||||||||||
| DE 017 820 97X | ||||||||||||||||||||
| Author(s): | ||||||||||||||||||||
| Chen, Mufa | ||||||||||||||||||||
| Shorttitle: | ||||||||||||||||||||
| Variational formulas and approximation theorems for the first eigenvalue in dimension one. | ||||||||||||||||||||
| Source: | ||||||||||||||||||||
| Sci. China, Ser. A 44, No. 4, 409 - 418 (2001). | ||||||||||||||||||||
| Classification: | ||||||||||||||||||||
Primary Classification:
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Secondary Classification: |
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Keywords:
| elliptic linear differential/difference operators; first Dirichlet/Neumann eigenvalues; the lowest eigenvalue; both-sided estimates | Review: | On a finite or semi-infinite interval the author considers a general superposition L of the first and second derivative with x-dependent coefficients and with Dirichlet or Neumann boundary condition in the origin. The work is a continuation of its seven (all self-) references [this makes it less easy to put this paper in broader context since just one of them (but Trans. Amer. Math Soc.!) is extra-territorial] but offers very nice results (their essence being well characterized by the title, and they look ``final"). Amazingly enough, these explicit bounds are complete (i.e., both-sided)! Three illustrative examples demonstrate their power in applications. The study is complemented by its discrete, Markov-chain parallel considering the birth-death process mediated by the purely second-order difference operator D (personally, I would recommend to read this supplement first). Remarks to the editors: |
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