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A transformation of almost periodic pseudodifferential operators to Fourier multiplier operators with operator-valued symbols
2009 (English)In: Rendiconti del Seminario Matematico, ISSN 0373-1243, Vol. 67, no 2, 247-269 p.Article in journal (Refereed) Published
Abstract [en]

We present results for pseudodifferential operators on Rd whose symbol a(·,x)is almost periodic (a.p.) for each x ∈ Rd and belongs to a Hörmander class Smr,d. We studya linear transformation a 7→ U(a) from a symbol a(x,x) to a frequency-dependent matrixU(a)(x)l,l′ , indexed by (l,l′) ∈ L×L where L is a countable set in Rd . The map a 7→ U(a) transforms symbols of a.p. pseudodifferential operators to symbols of Fourier multiplieroperators acting on vector-valued function spaces. We show that the map preserves operatorpositivity and identity, respects operator composition and respects adjoints.

Place, publisher, year, edition, pages
Turin: Univ. Torino Dip. Mat. , 2009. Vol. 67, no 2, 247-269 p.
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-27583OAI: oai:DiVA.org:lnu-27583DiVA: diva2:637385
Conference
Second Conf. Pseudo-Differential Operators
Available from: 2013-07-17 Created: 2013-07-17 Last updated: 2017-12-06Bibliographically approved

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Wahlberg, Patrik

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