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On evolution equations for lie groupoids
TL;DR: In this article, the authors studied the fundamental solution of the evolution equation (∂ ∂t + iP)u = 0 where P is a self adjoint elliptic order one G-pseudodifferential operator on the Lie groupoid G.
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Abstract: Using the calculus of Fourier integral operators on Lie groupoids developped in [18], we study the fundamental solution of the evolution equation (∂ ∂t + iP)u = 0 where P is a self adjoint elliptic order one G-pseudodifferential operator on the Lie groupoid G. Along the way, we continue the study of distributions on Lie groupoids done in [17] by adding the reduced C *-algebra of G in the picture and we investigate the local nature of the regularizing operators of [32].
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Citations
A fixed-point formula for Dirac operators on Lie groupoids
Ahmad Reza Haj Saeedi Sadegh,Shiqi Liu,Yiannis Loizides,Jesús Sánchez +3 more
- 20 Jul 2023
TL;DR: In this article , the authors studied equivariant families of Dirac operators on the source fibers of a Lie groupoid with a closed space of units and equipped with an auxiliary compact Lie group.
1
Fourier Integral Operators
Yu. V. Egorov,Mikhail Shubin +1 more
- 01 Jan 1994
TL;DR: In this paper, the Fourier integral operators (FIFO) were examined for hyperbolic types of elliptic differential equations, and a wider class of operators, the so-called FIFO-integral operators (Egorov [1975], Hormander [1968, 1971, 1983, 1985], Kumano-go [1982], Shubin [1978], Taylor [1981], Treves [1980]).
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TL;DR: In this paper, a more general class of pseudo-differential operators for non-elliptic problems is discussed. But their value is rather limited in genuinely nonelliptical problems.
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General theory of lie groupoids and lie algebroids
Kirill C. H. Mackenzie
- 01 Jun 2005
TL;DR: A comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry, in particular their relations with Poisson geometry and general connection theory, is given in this article.