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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,...

It is well known that for any smooth domain $\Omega\subset\mathbb{R}^N$ the energy functional (the one for which the Euler-Lagrange equation is our b.v.p.) associated to the following local problem: $$...

I have this situation: supposing that $\Omega$, is an open, bounded subset of $\mathbb{R}^N$, $N>2$. Given $t_0>0$ and $\overline{n}>0$, let's consider $\overline{t}=t_0+1$, $m>\overline{t}...

In this paper N. Ghoussoub, the author claims the following version of Marino–Prodi perturbation, that is : Let $H$ a Hilbert space. Let $f\in C^2(H, \mathbb{R}),$ $K$ is a compact subset of $K_c$ (...

I'm fairly new to functional calculus but and posting here since the question seems more appropriate than for MSE. When coming across this post I could not help but wonder the following. Let $H$ be ...

Suppose that $\mathcal{C}$ and $\mathcal{D}$ are subsets of $L^2(X,\Sigma,\mu)\cap L^{\infty}(X,\Sigma,\mu)$, where $\mu$ is a finite-measure on $(X,\Sigma)$. Let $F:L^2(X,\Sigma,\mu)\times L^2(X,\...