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Results tagged with ca.classical-analysis-and-odes
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user 50777
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
2
votes
Accepted
Solution of an ODE upon singular perturbation
Let me change the notations to fit the mathematical literature. I will denote by $x(t) \in \mathbb{R}^{3N}$ the positions of the particles, by $y(t) \in \mathbb{R}^{3N}$ their velocities and by $0 < \ …
- 981
3
votes
The compact embedding of $H^{1/2}_{2\pi}$ in $L^s(0, 2\pi)$
I would say that the book Linear and Quasilinear Parabolic Problems, Volume II: Function Spaces by Herbert Amann qualifies as a modern reference (published in 2019).
You can find a version of a Rellic …
- 981
1
vote
Accepted
Complex interpolation of subspaces
I believe this is indeed true, if, as mentioned in my comment, one assumes that $P$ is a contractive projection from $X_0 \to X_0$ and $X_1 \to X_1$ and defines $E_\theta := P X_\theta$ for all $\thet …
- 981
1
vote
Accepted
Constrained linear optimization problem on $C^1$
As you suggest, let me consider the case $f \equiv 1$. Without loss of generality, assume also that $a = 0$ and $b = 1$. Let $\sigma := o(1)/o(0) \in (0,1)$. The problem becomes
$$
\sup_{v \in C^1([0, …
- 981
2
votes
Bound for the product of Sobolev functions in $W^{s,1}$
I believe that $W^{s,1}(\mathbb{R}^d)$ is a Banach algebra when $s > d$.
This is a particular case of Theorem 7.3 of the paper Multiplication in Sobolev spaces by Ali Behzadan and Michael Holst.
- 981