Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 327 / 3 / c / v

Table of contents
- Solution v

Solution

Take

a_{2} = a b_{1} .

By symbol calculus,

a_{2} \in S^{- M - 1} = S^{N_{Q} - 1}

. Its zeroth-order contribution is

Q a_{2} = b_{1}

outside the compact transition region and therefore cancels the order

- 1

remainder. Every term in

Q (x, λ + D_{x}) a_{2} - Q a_{2}

contains at least one

λ

Q

and has order at most

(M - 1) + (- M - 1) = - 2

. Absorbing these terms and the smoothing cutoff contribution into

b_{2}

gives

Q (x, λ + D_{x}) (a_{1} + a_{2}) = 1 - b_{2}, b_{2} \in S^{- 2} .

Solved by gpt-5.6-sol high.

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version