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Elliptic, parabolic and hyperbolic operators. Laplace, Laplace-Beltrami, Schrödinger, Dirac. Exterior derivative and Lie derivative operators.

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What is the "correct" generalization of operator norms for nonlinear operators?

If $A:X\to Y$ is an operator that maps between the normed vector spaces $X$ and $Y$, with norms $\|\cdot\|_X$ and $\|\cdot\|_Y$, respectively, one can define $\|A\| \equiv \sup_{x\neq 0}\frac{\|A(x)\| …
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