Converse Sturm–Hurwitz–Kellogg theorem and related results
نویسنده
چکیده
We prove that if V n is a Chebyshev system on the circle and f is a continuous real-valued function with at least n + 1 sign changes then there exists an orientation preserving diffeomorphism of S that takes f to a function L-orthogonal to V . We also prove that if f is a function on the real projective line with at least four sign changes then there exists an orientation preserving diffeomorphism of RP that takes f to the Schwarzian derivative of a function on RP. We show that the space of piecewise constant functions on an interval with values ±1 and at most n + 1 intervals of constant sign is homeomorphic to n-dimensional sphere. Mathematics Subject Classification (2000).
منابع مشابه
0 71 0 . 59 02 v 1 [ m at h . D G ] 3 1 O ct 2 00 7 Converse Sturm - Hurwitz - Kellogg theorem and related results
We prove that if V n is a Chebyshev system on the circle and f(x) is a continuous function with at least n + 1 sign changes then there exists an orientation preserving diffeomorphism of S that takes f to a function L-orthogonal to V . We also prove that if f(x) is a function on the real projective line with at least four sign changes then there exists an orientation preserving diffeomorphism of...
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