Infinite order ΨDOs: composition with entire functions, new Shubin-Sobolev spaces, and index theorem

We study global regularity and spectral properties of power series of the Weyl quantisation a w , where a ( x , ξ ) is a classical elliptic Shubin polynomial. For a suitable entire function P , we associate two natural infinite order operators to a w , P ( a w ) and ( P ∘ a ) w , and prove that thes...

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