Expansion of traces and Dixmier traceability for global pseudo-differential operators on manifolds with boundary

Cardona D. Kumar V. Ruzhansky M. Tokmagambetov N.
July 2025 Birkhauser

Advances in Operator Theory
2025 #10 Issue 3

Given a smooth manifold M (with or without boundary), in this paper we study the regularisation of traces for the global pseudo-differential calculus in the context of non-harmonic analysis. Indeed, using the global pseudo-differential calculus on manifolds (with or without boundary) developed in Ruzhansky and Tokmagambetov (Int Math Res Not IMRN 12:3548–3615, 2016), the Calderón–Vaillancourt Theorem and the global functional calculus in Cardona et al. (Adv Oper Theory arXiv:2101.02519, 2020), we determine the singularity orders in the regularisation of traces and the sharp regularity orders for the Dixmier traceability of the global Hörmander classes. Our analysis (free of coordinate systems) allows us to obtain non-harmonic analogues of several classical results arising from the microlocal analysis of regularised traces for pseudo-differential operators with symbols defined by localisations.

Dixmier traces , Manifolds with boundary , Pseudo-differential operators , Regularised traces

Text of the article Перейти на текст статьи

Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Centre de Recerca Matemática, Edifici C, Campus Bellaterra, Bellaterra (Barcelona), 08193, Spain
Institute of Mathematics and Mathematical Modeling, 28 Schevchenko Str., Almaty, 050010, Kazakhstan
Al-Farabi Kazakh National University, 71 Al-Farabi Ave., Almaty, 050040, Kazakhstan

Department of Mathematics: Analysis
School of Mathematical Sciences
Centre de Recerca Matemática
Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026