On universality and convergence of the Fourier series of functions in the disc algebra

Continuous functions with universally divergent Fourier series on small subsets of the circle

It is shown that quasi all continuous functions on the unit circle have the property that, for many small subsets E of the circle, the partial sums of their Fourier series considered as functions restricted to E exhibit certain universality properties.

Multiplier Theorem for Fourier Series in continuous-discrete Sobolev orthogonal polynomials

In the paper we study the multipliers of Fourier series in polynomials orthogonal in continuous-discrete Sobolev's spaces. Multiplier Theorem for Fourier-Sobolev series is obtained. This result is based on the representation of the Fejér kernel, on the construction of the "humpbacked majorant" and weighted estimates of maximal functions.

单侧正交多项式与$SU(2)$值非线性傅里叶级数的一个逐点收敛结果

One sided orthogonal polynomials and a pointwise convergence result for $SU(2)$-valued nonlinear Fourier series

本文研究$SU(2)$值非线性傅里叶级数与单位圆上正交多项式的关系，证明再生核的普适性收敛结果，并建立多项式乘积逐点收敛与零点及局部参数的联系，最后在特定条件下证明沿缺项序列的几乎处处收敛。

The convergence of discrete Fourier-Jacobi series

The discrete counterpart of the problem related to the convergence of the Fourier-Jacobi series is studied. To this end, given a sequence, we construct the analogue of the partial sum operator related to Jacobi polynomials and characterize its convergence in the $\ell^p(\mathbb{N})$-norm.

从离散到连续非线性傅里叶变换的收敛性

Convergence from the discrete to the continuous non-linear Fourier transform

该研究借助复函数论与谱问题的关联新视角，探究离散到连续非线性傅里叶变换的收敛性，指出微分算子谱问题视角下的相关结果与离散情形的收敛问题具有相似性。