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I have an integral operator and I wonder how I can characterize the critical point. I'll give a simplified example so maybe people can comment on and I can maybe generalize in another question. Discla …

I recently came across the field of "Sparse representation". A talk is given here : https://www.youtube.com/watch?v=2bW4TkfTk-M. The goal of sparse representation is taking a signal and representing w …

Generally given an Hilbert space $X$ with and a bounded linear operator $H : X \to X$ given a vector $y \in X$ we seek an $x \in X$ such that $$ f(x) = \frac{1}{2} \left\lVert Hx - y \right\rVert_2^2 …

Follow up from this question Thin-Plate-Spline understanding and solution. In the general case of $\mathbb{R}^N$ the following problem (interpolant which minimizes the Thin Plate Energy, specifically …

It is known that the equation $$ \Delta f = 0 $$ on some bounded domain $\Omega$ on $\mathbb{R}^n$ subjected to certain boundary conditions can be derived through the minimization of the Dirichlet Ene …

I am trying to formulate a problem as a PDE. What I want to know is if my formulation is correct, if it admits solution and what am I missing. This question is related to : Thin-Plate-Spline understan …

Follow up question from this one Suppose $X = L^2(G)$, where $G$ is some locally compact group. Let $x, y \in G$ I for fixed $n$ I am seeking for an operator $H \in B(X)$ of the form $$ H = H(\alpha_1 …

This is a migrated question from: Thin-Plate-Spline understanding and solution. If I need to delete one of the questions let me know. I was suggested to post it here as well. As I understand it a Thin …