Automatic continuity of transversal distributions

Kališnik, J.

doi:10.1090/proc/16063

Automatic continuity of transversal distributions
HTML articles powered by AMS MathViewer

by J. Kališnik PDF

Proc. Amer. Math. Soc. 150 (2022), 5243-5251 Request permission

Abstract:

We prove that every transversal distribution on the fiber bundle $\pi _{M}:M\times N\to M$ is automatically continuous.

References

Iakovos Androulidakis and Georges Skandalis, Pseudodifferential calculus on a singular foliation, J. Noncommut. Geom. 5 (2011), no. 1, 125–152. MR 2746653, DOI 10.4171/JNCG/72
Erik van Erp and Robert Yuncken, A groupoid approach to pseudodifferential calculi, J. Reine Angew. Math. 756 (2019), 151–182. MR 4026451, DOI 10.1515/crelle-2017-0035
Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035, DOI 10.1007/978-3-642-96750-4
Andreas Kriegl and Peter W. Michor, The convenient setting of global analysis, Mathematical Surveys and Monographs, vol. 53, American Mathematical Society, Providence, RI, 1997. MR 1471480, DOI 10.1090/surv/053
Jean-Marie Lescure, Dominique Manchon, and Stéphane Vassout, About the convolution of distributions on groupoids, J. Noncommut. Geom. 11 (2017), no. 2, 757–789. MR 3669118, DOI 10.4171/JNCG/11-2-10
Jaak Peetre, Une caractérisation abstraite des opérateurs différentiels, Math. Scand. 7 (1959), 211–218 (French). MR 112146, DOI 10.7146/math.scand.a-10574
Jan Slovák, Peetre theorem for nonlinear operators, Ann. Global Anal. Geom. 6 (1988), no. 3, 273–283. MR 982996, DOI 10.1007/BF00054575
F. Tréves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967.