I consider the Laplacian operator $$A=-\Delta$$ in the domain $$H^2(\mathbb{R}^3)$$ where it is selfadjoint. We know that its spectrum is $[0,+\infty)$. Now I want to consider the restriction of $A$ to a given subspace of $H^2(\mathbb{R}^3)$. What can I say about the spectrum of this restriction?
2026-03-27 07:13:20.1774595600
Doubt about the spectrum of an operator
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