Rolle's Theorem for Polynomials of Degree Four in a Hilbert Space

Author: Ferrer J.

Source: Journal of Mathematical Analysis and Applications, Volume 265, Number 2, January 2002 , pp. 322-331(10)

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Abstract:

In 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. © 2002 Elsevier Science.

Keywords: Rolle'; s Theorem; Hilbert spaces; polynomials

Language: English

Document Type: Research article

Affiliations: Departamento de Análisis Matemático, Universidad de Valencia, Dr. Moliner 50, Valencia, 46100 Burjasot, Spain

Publication date: 2002-01-01