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Rolle's Theorem for Polynomials of Degree Four in a Hilbert Space
Jesús Ferrersubject
Hilbert spacesDiscrete mathematicsHilbert manifoldRolle's theorempolynomialsApplied MathematicsHilbert spaceHilbert's basis theoremCompact operator on Hilbert spacesymbols.namesakeVon Neumann's theoremHilbert schemeRolle's TheoremsymbolsBrouwer fixed-point theoremAnalysisMathematicsdescription
AbstractIn an infinite-dimensional real Hilbert space, we introduce a class of fourth-degree polynomials which do not satisfy Rolle's Theorem in the unit ball. Extending what happens in the finite-dimensional case, we show that every fourth-degree polynomial defined by a compact operator satisfies Rolle's Theorem.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-01-01 | Journal of Mathematical Analysis and Applications |