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Results tagged with ca.classical-analysis-and-odes
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user 6651
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
4
votes
Weighted Hardy Inequality for bounded domains
Sorry, I can't access the image on my browser; it won't load for some reason. Could you please type out the inequality in Latex?
So I'll just have to guess what you might want; apologies if this is n …
- 1,990
5
votes
Splines, harmonic analysis, singular integrals.
If you want to extend differentiation to all continuous functions, then (provided you have some convenient mathematical properties of the extension) you are FORCED to use distributions or roughly equi …
- 1,990
1
vote
On linear independence of exponentials
Still thinking about the interesting question!
Not an answer, but too big for a comment.
To show what I meant in my comment to Daniel Litt's answer about the difference between uniform absolute conv …
- 1,990
2
votes
The maximum of a real trigonometric polynomial
Even in the special case where $f(x) \geq 0$ for all $x$, there can't be any simple answer involving the coefficients $(a_n)$, $(b_n)$. You're basically asking to estimate the $L^\infty$ norm of a tri …
- 1,990
18
votes
1
answer
3k
views
Let a function f have all moments zero. What conditions force f to be identically zero?
Throughout, let $f$ be a Lebesgue measurable function (or continuous if you wish, but this is probably no easier). (Questions with distributions etc. are possible also but I want to keep things simple …
- 1,990
10
votes
When I can safely assume that a function is a Laplace transform of other function?
This kind of question is very interesting, and I too would like to know answers.
Sorry to self-publicise; I hope it's not regarded as impolite, but since I have also considered this exact kind of ques …
- 1,990