A note on the weak convergence of continuously integrable sequences

非勒贝格可积有界变差函数的二重傅里叶积分的反演

Inversin of double Fourier integral of non-Lebesgue integrable bounded variation functions

本研究针对非勒贝格可积有界变差函数，证明其截断二重傅里叶积分逐点收敛，推导得到非勒贝格可积函数的Dirichlet-Jordan定理，填补了该领域现有研究多聚焦勒贝格可积函数的空白。

On the lattice structure of the space of all Bochner integrable Banach lattice-valued functions

Suppose $(X,Σ,μ)$ is a finite measure space, $E$ is a Banach lattice, and $B(X,E,μ)$ is the space of all Bochner integrable $E$-valued functions. In this note, we show that $B(X,E,μ)$ is a $KB$-space or has the sequential Fatou property if and only if so is $E$. Among this, some results about Bochner integral convergence in $B(X,E,μ)$, using order structure of $E$, have been proved, as well.

Integrable operators and squares of Hankel Matrices

In this note, we find sufficient conditions for an operator with kernel of the form $A(x)B(y)-A(x)B(y)/(x-y)$ (which we call a Tracy-Widom type operator) to be the square of a Hankel operator. We consider two contexts: infinite matrices on $\ell^2$, and integral operators on the Hardy space $H^2(\mathbb{T})$. The results can be applied to the discrete Bessel kernel, which is significant in random matrix theory.

Stokes-type Integral Equalities for Scalarly Essentially Integrable Locally Convex Vector Valued Forms which are Functions of an Unbounded Spectral Operator

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 p…

Division subspaces and integrable kernels

In this note we prove that the reproducing kernel of a Hilbert space satisfying the division property has integrable form, is locally of trace class, and the Hilbert space itself is a Hilbert space of holomorphic functions.

收缩算子与耗散算子的实值谱移函数

Real-valued spectral shift functions for contractions and dissipative operators

本文针对收缩算子对与耗散算子对，公布了可积实值谱移函数存在性的充分条件，补充了此前迹类差收缩算子可积谱移函数存在性相关研究的实值性结论。