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Results tagged with ca.classical-analysis-and-odes
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user 317800
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
3
votes
Fourier transform of periodic distributions
This is a comment rather than an answer but it will be too long. There is a confusion in your statement which I find rather irritating and which has not, as far as I can see, been addressed here. I …
- 406
1
vote
Are there any nonlinear solutions to $f(x+1) - f(x) = f'(x)$?
After this question popped up again, it seemed to me to scream out for a use of the Fourier Transform (FT). I have decided to post this as an answer, since this approach is transparent and provides a …
- 406
1
vote
What do we know about the space of finite order distributions ?
The following are some night thoughts on finite order distributions which might be of interest since this topic is a rich source of fruitful questions on the relations between abstract functional anal …
- 406
1
vote
Fourier transform of a generalized function on the plane
Chanced on this and after much rumination I have decided to point out the following flaws in the postings.
Firstly, I assume that when you write $$\frac 1 {x+y^2+i0}$$ you mean a limit of the functio …
- 406
0
votes
What well known results with countability assumptions can be naturally extended to uncountab...
This is a riff on this query, concentrating on aspects of functional analysis and related topics. It is formulated in a conversational manner but is based on the concepts of ind and pro categories wh …
0
votes
Distributions as derivatives
This is perhaps tangential to your query but I am posting it in the hope that it might contain useful information. I will start with the case of distributions on a compact interval, which we can assu …
- 406