Liftings for ultra-modulation spaces, and one-parameter groups of Gevrey-type pseudo-differential operators

• We deduce one-parameter group properties for pseudo-differential operators Op(a), where a belongs to the class Λ∗(ω0) of certain Gevrey symbols. We use this to show that there are pseudo-differential operators Op(a) and Op(b) which are inverses to each other, where a ∈ Λ∗(ω0) and b ∈ Λ∗(1/ω0). We apply these results to deduce lifting property for modulation spaces and construct explicit isomorphisms between them. For each weight functions ω,ω0 moderated by GRS submultiplicative weights, we prove that the Toeplitz operator (or localization operator) Tp(ω0) is an isomorphism from Mp,q(ω) to M(ω/ω0)p,q for every p,q ∈(0,∞]. © 2019 World Scientific Publishing Company.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Banach function spaces

comparable symbols

confinement of symbols

Gelfand-Shilov spaces

symbol-valued evolution equations

Toeplitz operators

ultra-distributions

Mathematics

Matematik

Publication and Content Type

ref (subject category)

art (subject category)