Vector-valued oscillatory integrals and $(\rho,\delta)$-type pseudodifferential calculusOberseminar Global Analysis and Operator Algebras

by Gihyun Lee (University of Potsdam)

Tuesday Nov 4, 2025, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60/1-008 (Mathezentrum)

I shall report on ongoing joint work with Vishvesh Kumar (Ghent
University, Belgium), in which we construct a general pseudodifferential calculus of
type $(\rho,\delta)$ associated with symbols taking values in a locally convex
space. Our framework covers the classical Kohn-Nirenberg and Weyl calculi, while our
main motivation is to generalize Connes’ pseudodifferential calculus on
noncommutative tori to the general $(\rho,\delta)$-type. I will introduce the
vector-valued oscillatory integral underlying our construction and discuss the
technical difficulties that do not appear in the scalar- or Banach space-valued
$(\rho,\delta)$-type calculi in the literature. If time permits, the
$L^p$-boundedness of pseudodifferential operators on noncommutative tori will also
be presented.