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Questions tagged [ca.classical-analysis-and-odes]

Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

2,268 questions
27 views

On the convergence of a sqeuence of functions with decomposition

Considering a sequence of function $f_n(x,y)$ converges to $F(x,y)$ as $n\to+\infty$, we also know that the function $f_n(x,y)$ can be decoupled as the summation of two functions with $x$, $y$ as ...
146 views

A Fredholm equation with a particular kernel

How to solve this kind of Fredholm’s equation? $$x(t)+\lambda \int\limits_{0}^{1}\! \big[ts - \min\{t,s\}\big]x(s)ds=t$$ Thanks for any help.
226 views

Sub-Gaussian decay of convolution of $L^1$ function with Gaussian kernel

I think it might be helpful to put the new statement at the beginning and put the original post at the end. This new statement is more mathematically elegant. Let $f\geq0$ be in $L^1(\mathbb{R}^d)$ ...
66 views

How can I solve this issue? [closed]

I have a problem related to this theme system analysis and action research. If you can please solve this, in another case please take me more resource for understanding this. The system consists of N-...
72 views

Relation between the measures of two sets defined via Lebesgue integration

I posted this question on StackExchange, people have upvoted it but I have not received any response. I read up here that it is okay to post unanswered StackExchange questions on Mathoverflow. So, ...
89 views

Stability analysis of a differential equation

My question is about stability analysis and whether the equilibrium point is well-defined in example 2?. If they are not defined, how can one approach the stability analysis for those cases. Example ...
77 views

Estimate on first derivatives given $L^2$-norm of Laplacian

Let $B$ be the unit ball in the Euclidean space $\mathbb{R}^n$. Consider the set of functions $$X=\{u\in C^2(\bar B) \mid u|_{\partial B}=0 \text{ and } \|\Delta u\|_{L^2(B)}\leq 1\},$$ where $\Delta$ ...
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Under what conditions is this family normal?

Let $\mathcal{S} = \{s \in \mathbb{C}\,\mid\,|\Im(s)| < 1\}$ be a strip of the complex plane. Let $q(s,z)$ be a holomorphic function on $\mathcal{S} \times \mathbb{C}$. Letting $\mathcal{K}$ be a ...
159 views

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Help me prove this is identically zero! [duplicate]

I am having trouble with the definition of functional derivatives to see that the following expression is zero. The expression is: \int{\nabla \left(\frac{\delta F}{\delta B}\times \frac{\delta G}{...
34 views

Derivatives of descriptors with respect to cartesian coordinates

I am trying to take the derivatives of some complicated descriptors in order to derive forces for usage in molecular dynamics. We start with a "lab frame" of cartesian coordinates, with a system of $N$...

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