21 citations · 23 across the 8 of their papers we have counts for
8 papers
Observability and controllability for the Schrödinger equation on polyhedra
Wei Qu, Zhiwen Duan
We consider the observability and controllability for the Schrödinger equation on polyhedra. We show that for the Schrödinger equation on convex polyhedra in $\mathbb{R}^d\,(d\geq2…
The sparse representation related with fractional heat equations
Pengtao Li, Tao Qian, Ieng Tak Leong +1
This study introduces pre-orthogonal adaptive Fourier decomposition (POAFD) to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and t…
AFD Types Sparse Representations vs. the Karhunen-Loeve Expansion for Decomposing Stochastic Processes
Tao Qian, Ying Zhang, Wanquan Liu +1
This article introduces adaptive Fourier decomposition (AFD) type methods, emphasizing on those that can be applied to stochastic processes and random fields, mainly including stoc…
Sparse Representations of Solutions to a class of Random Boundary Value Problems
Fang Yang, Min Chen, Jiecheng Chen +2
We introduce certain sparse representation methods, named as stochastic pre-orthogonal adaptive Fourier decomposition 1 and 2 (SPOAFD1 and SPOAFD2) to solve the Dirichlet boundary…
Phase Retrieval in Hardy Space
Wei Qu, Xiao-Yun Sun, Guan-Tie Deng
This paper concerns the study of reconstructing a function in the Hardy space of the unit disc $\D$ from intensity measurements $|f(z)|,\ z\in \D.$ It's known as the problem of…
Sparse Approximation to the Dirac-δ Distribution
Wei Qu, Tao Qian, Guan-Tie Deng
The Dirac-δ distribution may be realized through sequences of convlutions, the latter being also regarded as approximation to the identity. The present study proposes the so called…
A sufficient condition for n-Best Kernel Approximation in Reproducing Kernel Hilbert Spaces
Wei Qu, Tao Qian, Guan-Tie Deng
We show that if a reproducing kernel Hilbert space consisting of functions defined on enjoys Double Boundary Vanishing Condition (DBVC) and Linear Independent Con…
Rational Approximation in the Bergman Spaces
Wei Qu, Pei Dang
It is known that adaptive Fourier decomposition (AFD) offers efficient rational approxima- tions to functions in the classical Hardy H2 spaces with significant applications. This s…