Continuity Properties of Multilinear Localization Operators on Modulation Spaces

  • Nenad TeofanovEmail author
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


We introduce multilinear localization operators in terms of the short-time Fourier transform and multilinear Weyl pseudodifferential operators. We prove that such localization operators are in fact Weyl pseudodifferential operators whose symbols are given by the convolution between the symbol of the localization operator and the multilinear Wigner transform. To obtain such interpretation, we use the kernel theorem for the Gelfand–Shilov space \( {\mathscr {S}}^{( 1)} (\mathbb {R}^d) \) and its dual space of tempered ultra-distributions \( {\mathscr {S}}^{( 1)'} (\mathbb {R}^{2d})\). Furthermore, we study the continuity properties of the multilinear localization operators on modulation spaces. Our results extend some known results when restricted to the linear case.



This research is supported by MPNTR of Serbia, project numbers 174024 and DS 028 (TIFMOFUS).


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Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsUniversity of Novi SadNovi SadSerbia

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