Geodesic
Stokes-type integral equalities for scalarly essentially integrable locally convex vector-valued forms which are functions of an unbounded spectral operator
Eurasian mathematical journal, Tome 12 (2021) no. 3, pp. 78-89.

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In this work we establish a Stokes-type integral equality for scalarly essentially integrable forms on an orientable smooth manifold with values in the locally convex linear space $\langle B(G),\sigma(B(G),\mathcal{N})\rangle$, where $G$ is a complex Banach space and $\mathcal{N}$ is a suitable linear subspace of the norm dual of $B(G)$. This result widely extends the Newton-Leibnitz-type equality stated in one of our previous articles. To obtain our equality we generalize the main result of those articles, and employ the Stokes theorem for smooth locally convex vector-valued forms established there. Two facts are remarkable. First, the forms integrated involved in the equality are functions of a possibly unbounded scalar-type spectral operator in $G$. Secondly, these forms need not be smooth nor even continuously differentiable. 
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B. Silvestri. Stokes-type integral equalities for scalarly essentially integrable locally convex vector-valued forms which are functions of an unbounded spectral operator. Eurasian mathematical journal, Tome 12 (2021) no. 3, pp. 78-89. http://geodesic.mathdoc.fr/item/EMJ_2021_12_3_a7/

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[3] B. Silvestri, Integral equalities for functions of unbounded spectral operators in Banach spaces, Dissertationes Math., 464, 2009, 60 pp. | DOI | Zbl

[4] B. Silvestri, Scalarly essentially integrable locally convex vector-valued tensor fields. Stokes theorem, arXiv: 2010.02327