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Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.

2 votes

Show that the Laplacian operator on the Heisenberg group is negative

The factorization of the Heisenberg Laplacian is well known, see http://www.scirp.org/journal/PaperDownload.aspx?paperID=22807
Fan Zheng's user avatar
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3 votes
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$L^2$ function in Schwartz space?

This is quite ad hoc, but your integral equation can be reverse engineered to a differential equation (Maybe this is what you really want to solve?) $$ \partial_t\varphi=\alpha(t)f\varphi,\ \varphi(0 …
Fan Zheng's user avatar
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