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Results tagged with differential-equations
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user 359
Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
4
votes
5
answers
882
views
Analytic hypoellipticity of linear ordinary differential operators
Let $P = a_n(x) D_x^n + a_{n-1}(x) D_x^{n-1} + \ldots + a_0(x)$ be a linear ordinary differential operator with polynomial (or real analytic) coefficients $a_j(x)$. Suppose that $a_n(x)$ doesn't vanis …
- 1,412
4
votes
Getting a differential equation for a function from a functional equation of its Mellin tran...
By defining the Mellin transform for distributions as for instance done in Transform Analysis of Generalized Functions by O. Misra, J. Lavoine it follows that the functional equation for $F(s)$ transl …
- 1,412
17
votes
2
answers
2k
views
Getting a differential equation for a function from a functional equation of its Mellin tran...
If $f$ is a locally integrable function then its Mellin transform
$\mathcal{M}[f]$ is defined by
$$ \mathcal{M}[f] (s) = \int_0^{\infty} x^{s - 1} f (x) dx . $$
This integral usually converges in a st …
- 1,412