Abstract
AbstractFor any smooth, Hausdorff and second-countable manifold N one can define the Fréchet space $$\mathord {\mathcal {C}^{\infty }}(N)$$
C
∞
(
N
)
of smooth functions on N and its strong dual $$\mathcal {E}'(N)$$
E
′
(
N
)
of compactly supported distributions on N. It is a standard result that the strong dual of $$\mathcal {E}'(N)$$
E
′
(
N
)
is naturally isomorphic to $$\mathord {\mathcal {C}^{\infty }}(N)$$
C
∞
(
N
)
, which implies that both $$\mathord {\mathcal {C}^{\infty }}(N)$$
C
∞
(
N
)
and $$\mathcal {E}'(N)$$
E
′
(
N
)
are reflexive locally convex spaces. In this paper we generalise that result to the setting of transversal distributions on the total space of a surjective submersion $$\pi :P\rightarrow M$$
π
:
P
→
M
. We show that the strong $$\mathord {\mathcal {C}^{\infty }_{c}}(M)$$
C
c
∞
(
M
)
-dual of the space $$\mathcal {E}'_{\pi }(P)$$
E
π
′
(
P
)
of $$\pi $$
π
-transversal distributions is naturally isomorphic to the $$\mathord {\mathcal {C}^{\infty }_{c}}(M)$$
C
c
∞
(
M
)
-module $$\mathord {\mathcal {C}^{\infty }}(P)$$
C
∞
(
P
)
.
Publisher
Springer Science and Business Media LLC
Reference16 articles.
1. Androulidakis, I., Skandalis, G.: Pseudodifferential calculus on a singular foliation. J. Noncommut. Geom. 5, 125–152 (2011)
2. Androulidakis, I., Mohsen, O., Yuncken, R.: The convolution algebra of Schwarz kernels on a singular foliation. J. Oper. Theory 85(2), 475–503 (2021)
3. Androulidakis, I., Mohsen, O., Yuncken, R.: A pseudodifferential calculus for maximally hypoelliptic operators and the Helffer–Nourrigat conjecture. arXiv:2201.12060
4. Debord, C., Skandalis, G.: Adiabatic groupoid, crossed product by $${\mathbb{R} }^{*}_{+}$$ and pseudodifferential calculus. Adv. Math. 257, 66–91 (2014)
5. Horváth, J.: Topological Vector Spaces, vol. I. Addison-Wesley Series in Mathematics, p. XII. Addison-Wesley Publishing Company, London (1966)
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