A corrected quantitative version of the Morse lemma
نویسندگان
چکیده
منابع مشابه
A quantitative version of the Blow-up Lemma
In this paper we give a quantitative version of the Blow-up Lemma.
متن کاملThe Morse Lemma for Banach Spaces
REMARK. The above theorem is a classical result of Marston Morse in the case that V is finite dimensional and was generalized by the author to the case that F is a Hubert space [ l ] , [3]. The latter proof makes use of operator theory in Hubert space and does not extend in any obvious way to more general Banach spaces. The proof we give below is completely elementary and works for arbitrary V ...
متن کاملThe Morse Lemma on Banach Spaces
Let /: U-*R be a C3 map of an open subset U of a Banach space E. Letp £ U be a critical point of/ (df¡,=0). If £ is a conjugate space (E=F*) we define what it means for/» to be nondegenerate. In this case there is a diffeomorphism y of a neighborhood of p with a neighborhood of 0 E E, y(p)=0 with foy->(x) = id%(x,x)+f(p). In this paper we define a notion of nondegeneracy for critical points of ...
متن کاملA Constrained version of Sauer’s Lemma
Sauer’s Lemma is extended to classes H of binary-valued functions on [n] = {1, . . . , n} which have a margin less than or equal to N on x ∈ [n], where the margin μh(x) of a binary valued function h at a point x ∈ [n] is defined as the largest nonnegative integer a such that h is constant on the interval Ia(x) = [x−a, x+a] ⊆ [n]. Estimates are obtained for the cardinality of classes of binary v...
متن کاملThe Morse Lemma in Infinite Dimensions via Singularity Theory
An infinite dimensional Morse lemma is proved using the deformation lemma from singularity theory. It is shown that the versions of the Morse lemmas due to Palais and Tromba are special cases. An infinite dimensional splitting lemma is proved. The relationship of the work here to other approaches in the literature in discussed. Introduction. This paper shows that when the singularity theory pro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2019
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2019.02.021