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Results tagged with pseudo-differential-operators
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user 4362
This tag is for questions regarding to the Pseudo-differential operator, acting on a space of functions on a differentiable manifold, that can locally be described by definite rules using a certain function. It satisfies estimates for the derivatives analogous to the estimates for derivatives of polynomials, which are symbols of differential operators.
53
votes
Motivation for and history of pseudo-differential operators
I don't know the history at all, but I have to imagine that the language was invented to provide a context for talking about solution operators for differential equations. Consider, for example, the …
- 29.2k
14
votes
Applications of Atiyah-Singer using pseudodifferential operators
Index theory is fundamentally about a homomorphism
$$K_n(M) \to \mathbb{Z}$$
from the top degree K-homology of $M$ (even dimensional) to the integers called the analytic index map. It is called this …
- 29.2k
5
votes
Understanding the analytic index map of the Atiyah-Singer index theorem
I can't give you an answer that is well-adapted to Lawson and Michelsohn's formulation of the pseudodifferential calculus. But here's how this sort of argument is supposed to go: two elliptic pseudod …
- 29.2k