论文标题
斯塔克斯型的积分不可或缺
Stokes-type Integral Equalities for Scalarly Essentially Integrable Locally Convex Vector Valued Forms which are Functions of an Unbounded Spectral Operator
论文作者
论文摘要
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 $\langle B(G),σ(B(G),\mathcal{N})\rangle$, where $G$ is a complex Banach space and $\mathcal{N}$ is a suitable linear subspace of the norm $ b（g）$的双重。这一结果广泛扩展了我们以前的文章之一中所述的牛顿 - 莱布尼兹型平等。为了获得我们的平等，我们概括了该文章的主要结果，并采用了stokes定理，以使原始论文中建立的平滑局部凸价值形式。两个事实是显着的。首先，涉及平等的表单是$ g $中可能无限的标量频谱运算符的函数。其次，这些形式不必平滑，甚至不断地差异。
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 $\langle B(G),σ(B(G),\mathcal{N})\rangle$, 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 that article, and employ the Stokes theorem for smooth locally convex vector valued forms established in a prodromic paper. Two facts are remarkable. Firstly 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.
