Geodesic
Laplacians on Smooth Distributions as $C^*$-Algebra Multipliers
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical physics, Tome 152 (2018), pp. 67-90

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In this paper, we continue the study of spectral properties of Laplacians associated with an arbitrary smooth distribution on a compact manifold started in a previous paper. Under the assumption that the singular foliation generated by the distribution is smooth, we prove that the Laplacian associated with the distribution defines an unbounded, regular, self-adjoint operator in some Hilbert module over the $C^*$-algebra of the foliation.
Mots-clés : foliation, multiplier.
Keywords: Hilbert module, Laplacian, hypoelliptic operator, smooth distribution 
@article{INTO_2018_152_a6,
     author = {Yu. A. Kordyukov},
     title = {Laplacians on {Smooth} {Distributions} as $C^*${-Algebra} {Multipliers}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {67--90},
     publisher = {mathdoc},
     volume = {152},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_152_a6/}
}
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Yu. A. Kordyukov. Laplacians on Smooth Distributions as $C^*$-Algebra Multipliers. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical physics, Tome 152 (2018), pp. 67-90. http://geodesic.mathdoc.fr/item/INTO_2018_152_a6/