ϕ-equivalence of Amplitudes Sample Clauses

ϕ-equivalence of Amplitudes. ‌ In the local coordinates case we noticed that the map that associates an amplitude with a ΨDO is highly not injective, while it is essentially bijective if we restrict the domain to the class of symbols. In other words, given an amplitude, we can always associate a symbol defining the same ΨDO modulo a smoothing operator. Proposition 1.15 gives us an account of this technique. This section is devoted to replicating this result in the new context introduced in Chapter 3. The standard results in local coordinates concerning how to obtain from a given amplitude an equivalent symbol rely on Xxxxxx’x formula. They use integration by parts and the equality
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