Jump to ContentJump to Main Navigation
Show Summary Details

Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

IMPACT FACTOR increased in 2015: 1.616
5-year IMPACT FACTOR: 1.690
Rank 18 out of 312 in category Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 3.614
Source Normalized Impact per Paper (SNIP) 2015: 1.901
Impact per Publication (IPP) 2015: 1.302

Mathematical Citation Quotient (MCQ) 2015: 1.53

See all formats and pricing
Select Volume and Issue


30,00 € / $42.00 / £23.00

Get Access to Full Text

Pseudodifferential operators on locally compact abelian groups and Sjöstrand's symbol class

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2007, Issue 613, Pages 121–146, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2007.094, February 2008

Publication History

Published Online:


We investigate pseudodifferential operators on arbitrary locally compact abelian groups. As symbol classes for the Kohn-Nirenberg calculus we introduce a version of Sjöstrand's class. Pseudodifferential operators with such symbols form a Banach algebra that is closed under inversion. Since “hard analysis” techniques are not available on locally compact abelian groups, a new time-frequency approach is used with the emphasis on modulation spaces, Gabor frames, and Banach algebras of matrices. Sjöstrand's original results are thus understood as a phenomenon of abstract harmonic analysis rather than “hard analysis” and are proved in their natural context and generality.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Fawwaz Batayneh and Mishko Mitkovski
Journal of Fourier Analysis and Applications, 2015
Qiyu Sun
Applied and Computational Harmonic Analysis, 2008, Volume 25, Number 2, Page 148
Marius Măntoiu and Radu Purice
Journal of Pseudo-Differential Operators and Applications, 2012, Volume 3, Number 3, Page 283
Karlheinz Gröchenig and Joachim Toft
Journal d'Analyse Mathématique, 2011, Volume 114, Number 1, Page 255
Qiyu Sun
Constructive Approximation, 2011, Volume 34, Number 2, Page 209

Comments (0)

Please log in or register to comment.