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Let $M$ be a compact smooth manifold, $(\lambda_n)_{n=1}^{\infty}$ be a square-summable monotonically increasing sequence of non-negative numbers, and let $(f_k)_{k=1}^{\infty}$ be continuous ...

Let $\Omega \subset \mathbb R^2$ be a bounded domain with a smooth boundary. Let $$\bar{\partial}= \frac{1}{2} ( \partial_{x^1} + i \,\partial_{x^2}),$$ and let $G: L^2(\Omega)\to H^2(\Omega)$ be the ...

This might be considered as a continuation of my previous question Spectrum of a linear elliptic operator but is independent. I have another question on V. Gribov's paper "Quantization of non-Abelian ...

In the paper in quantum fields theory by Gribov,V.; (1978) "Quantization of non-Abelian gauge theories". Nuclear Physics B. 139: 1–19; in Section 3 the author makes the following claim from PDE and ...

Suppose $\Omega$ is a smooth bounded domain in $\mathbb{R}^3$. Consider the Newton potential \begin{equation} T [\phi](x) = \int_{\Omega} \frac{1}{|x-y|} \phi(y)dy. \end{equation} It is well know ...