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Results tagged with real-analysis
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user 2508
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
3
votes
How can I measure the Morse index in infinite dimensions?
It seems that simply one can't measure it. Here below is briefly described
an example of a nondegenerate indefinite inner product space having
no cardinal-valued Morse index.
Consider $(\ell^{2},<.,. …
- 4,060
2
votes
Splitting a space into positive and negative parts
Statement 1. is generally not true when V is infinite-dimensional.
For, let L be an infinite-dimensional real vector space, and let L* be
its algebraic dual. Put V := L x L*, and define a: V x V --> …
- 4,060
21
votes
solving $f(f(x))=g(x)$
Q2) has a negative answer. Namely, if, e.g., $g(x)=-x$ for all $x\in\mathbb{R}$,
then there is no
continuous
$f:\mathbb{R\rightarrow\mathbb{R}}$ such
that $f\circ f=g$.
As to Q3, see, e.g., Theor …
- 4,060