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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

3 votes
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289 views

Domain of Laplacian

Let $L$ be an operator on $C^2(\mathbb R)$, defined by $$L \phi (x) = \int_{|y|<1} (\phi(x+y) - \phi(x) - \phi'(x) \ y)\ \nu(dy), \text{ for all } x\in \mathbb R$$ for a measure $\nu(dy) = |y|^{-2} dy …
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