We show that the fourth degree polynomials that satisfy Rolle’s Theorem in the unit ball of a real Hilbert space are dense in the space of polynomials that vanish in the unit sphere. As a consequence, we obtain a sort of approximate Rolle’s Theorem for those polynomials.
Cite this article
Jesús Ferrer, An Approximate Rolle’s Theorem for Polynomials of Degree Four in a Hilbert Space. Publ. Res. Inst. Math. Sci. 41 (2005), no. 2, pp. 375–384DOI 10.2977/PRIMS/1145475359