适合于空间曲线的乘积核

广义积分算子与Schwartz核定理

Generalized Integral Operators and Schwartz Kernel Theorem

结合经典的Schwartz核定理，我们证明了在Colombeau广义函数的框架下，一大类线性映射允许积分核.为此，我们需要引入慢增长的广义函数的新空间和相应的适应线性映射。最后，我们证明了Schwartz的结果在某种意义上包含在我们的主要定理中.

The angle along a curve and range-kernel complementarity

In this paper, we define the angle of a bounded linear operator $A$ along an unbounded path emanating from the origin and use it to characterize range-kernel complementarity. In particular we show that if $0$ faces the unbounded component of the resolvent set, then $X=R(A)\oplus N(A)$ if and only if $R(A)$ is closed and some angle of $A$ is less than $π$.

Gelfand-Shilov空间，结构与核定理

Gelfand-Shilov spaces, Structural and Kernel theorems

最近的研究表明，与Gelfand Shilov空间同构的空间非常适合于在具有基本长度的量子场论中使用。我们相信所有的Gelfand Shilov空间，特别是那些具有拟解析检验函数空间的空间，都是量子场论的好的研究领域。该理论需要广义函数理论的技术成果，而不仅仅是微分学和定义良好的傅立叶变换，而且还需要核定理和结构定理。本文给出了Roumieu型和Beurling型Gelfand-Shilov空间的结构（正则性）定理和核定理。

Singular integrals on regular curves in the Heisenberg group

Let $\mathbb{H}$ be the first Heisenberg group, and let $k \in C^{\infty}(\mathbb{H} \, \setminus \, \{0\})$ be a kernel which is either odd or horizontally odd, and satisfies $$|\nabla_{\mathbb{H}}^{n}k(p)| \leq C_{n}\|p\|^{-1 - n}, \qquad p \in \mathbb{H} \, \setminus \, \{0\}, \, n \geq 0.$$ The simplest examples include certain Riesz-type kernels first considered by Chousionis and Mattila, and the horizontally odd kernel $k(p) = \nabla_{\mathbb{H}} \log \|p\|$. We prove that convolution with $k$, as above, yields an $L^{2}$-bounded operator on regular curves in $\mathbb{H}$. This extends a…