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Results tagged with ca.classical-analysis-and-odes
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user 5506
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
9
votes
1
answer
2k
views
If $f$ is $C^{\infty}$ and $f^2$ is analytic, then $f$ is analytic
Assume that $f:\mathbb{C}^n\rightarrow \mathbb{C}$ is a $C^{\infty}$ function such that $f^2$ is (complex) analytic. Then one can show that $f$ is analytic. (Note: Liviu Nicolaescu and Alexandre Ereme …
- 807
7
votes
Why is differentiating mechanics and integration art?
This is a collection of a few ideas. Let me see where it takes us.
It is probably too verbose since I am writing it as I think the question.
Maybe later I can shorten it and correct errors.
If you ar …
- 807
2
votes
0
answers
131
views
Representing quasianalytic functions in several variables
For functions in a quasianalytic Denjoy-Carleman class we have the property that their Taylor expansions at a point (the origin) determines the function. For classes that don't only contain analytic f …
- 807
1
vote
Factoring and solving trinomials
Factor where? Over the rationals? Take a look to Berlekamp algorith.
http://en.wikipedia.org/wiki/Berlekamp%27s_algorithm
The right link is http://en.wikipedia.org/wiki/Berlekamp%E2%80%93Zassenhaus_ …
- 807
2
votes
The Fundamental Theorem of Calculus in Lebesgue Theory
For every function $f$ with $f'$ integrable there is a function $g$ equal to $f$ everywhere but a point such that $\int_{a}^{b}g'dx=g(b)-g(a)$. Take $g(x)=f(x)$ for $x$ different from $b$ and $g(b)=\i …
- 807