A symplectic restriction problem

We investigate the norm of a degree 2 Siegel modular form of asymptotically large weight whose argument is restricted to the 3-dimensional subspace of its imaginary part. On average over Saito–Kurokawa lifts an asymptotic formula is established that is consistent with the mass equidistribution conjecture on the Siegel upper half space as well as the Lindelöf hypothesis for the corresponding Koecher–Maaß series. The ingredients include a new relative trace formula for pairs of Heegner periods.

SAR Target Classification Based on Sample Spectral Regularization

Synthetic Aperture Radar (SAR) target classification is an important branch of SAR image interpretation. The deep learning based SAR target classification algorithms have made remarkable achievements. But the acquisition and annotation of SAR target images are time-consuming and laborious, and it is difficult to obtain sufficient training data in many cases. The insufficient training data can make deep learning based models suffering from over-fitting, which will severely limit their wide application in SAR target classification. Motivated by the above problem, this paper employs transfer-learning to transfer the prior knowledge learned from a simulated SAR dataset to a real SAR dataset. To overcome the sample restriction problem caused by the poor feature discriminability for real SAR data. A simple and effective sample spectral regularization method is proposed, which can regularize the singular values of each SAR image feature to improve the feature discriminability. Based on the proposed regularization method, we design a transfer-learning pipeline to leverage the simulated SAR data as well as acquire better feature discriminability. The experimental results indicate that the proposed method is feasible for the sample restriction problem in SAR target classification. Furthermore, the proposed method can improve the classification accuracy when relatively sufficient training data is available, and it can be plugged into any convolutional neural network (CNN) based SAR classification models.

Sets of p-restriction and p-spectral synthesis

In this paper we investigate the restriction problem. More precisely, we give sufficient conditions for the failure of a set E in ℝn to have the p-restriction property. We also extend the concept of spectral synthesis to Lp(ℝn) for sets of p-restriction when p > 1. We use our results to show that there are p-values for which the unit sphere is a set of p-spectral synthesis in ℝn when n ⩾ 3.