A Transformation of Almost Periodic Pseudodifferential Operators to Fourier Multiplier Operators with Operator-valued Symbols
نویسنده
چکیده
We present results for pseudodifferential operators on Rd whose symbol a(·,ξ) is almost periodic (a.p.) for each ξ ∈ Rd and belongs to a Hörmander class Sm ρ,δ. We study a linear transformation a 7→ U(a) from a symbol a(x,ξ) to a frequency-dependent matrix U(a)(ξ)λ,λ′ , indexed by (λ,λ′) ∈ Λ×Λ where Λ is a countable set in Rd . The map a 7→ U(a) transforms symbols of a.p. pseudodifferential operators to symbols of Fourier multiplier operators acting on vector-valued function spaces. We show that the map preserves operator positivity and identity, respects operator composition and respects adjoints.
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