Fredholm theory connected with a Douglis-Nirenberg system of differential equations over $\mathbb{R}^n$

M. Faierman

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arXiv · 1612.08655

Fredholm theory connected with a Douglis-Nirenberg system of differential equations over $\mathbb{R}^n$

M. Faierman

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Abstract

We consider a spectral problem over $\mathbb{R}^n$ for a Douglis-Nirenberg system of differential operators under limited smoothness assumptions and under the assumption of parameter-ellipticity in a closed sector $\mathcal{L}$ in the complex plane with vertex at the origin. We pose the problem in an $L_p$ Sobolev-Bessel potential space setting, $1 < p < \infty$, and denote by $A_p$ the operator induced in this setting by the spectral problem. We then derive results pertaining to the Fredholm theory for $A_p$ for values of the spectral parameter $\lambda$ lying in $\mathcal{L}$ as well as results pertaining to the invariance of the Fredholm domain of $A_p$ with $p$.

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M. Faierman. 2016-12-27. Fredholm theory connected with a Douglis-Nirenberg system of differential equations over $\mathbb{R}^n$. https://arxiv.org/abs/1612.08655

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