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

✍ Scribed by Jesús Ferrer

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 91 KB
Volume: 265
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7708

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✦ Synopsis

In an infinite-dimensional real Hilbert space, we introduce a class of fourthdegree 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.

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