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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.

5 votes
1 answer
226 views

Why do people study Weyl asymptotics and partial-spectral-projections?

The major focus of the research that my advisor has me doing centers around the idea of asymptotic behavior of partial-spectral-projections on compact manifolds. In a few sentences, here is the contex …
1 vote
0 answers
243 views

Interpretation of Smoothing Operators as $\Psi$DO's

In most of the computations I've seen involving pseudodifferential operators (referred to as $\Psi$DO's from now on) we do not have true equality. Instead we often only have equivalence of operators, …