We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at their zero sets, thus obtaining explicit constants in a result of Levin. The estimates are then used to derive expl...We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at their zero sets, thus obtaining explicit constants in a result of Levin. The estimates are then used to derive explicit lower bounds for exponential Riesz bases, as they arise in Avdonin's Theorem on 1/4 in the mean or in a Theorem, of Bogmtr, Horvath, Job and Seip. An application is discussed, where knowledge of explicit lower bounds of exponential Riese bases is desirable.展开更多
We characterize a class of piecewise linear spectral sequences. Associated with the spectral sequence, we construct an orthonormal exponential bases for L2（[0,1）d）, which are called generalized Fourier bases. Moreo...We characterize a class of piecewise linear spectral sequences. Associated with the spectral sequence, we construct an orthonormal exponential bases for L2（[0,1）d）, which are called generalized Fourier bases. Moreover, we investigate the convergence of Bochner-Riesz means of the generalized Fourier series.展开更多
文摘We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at their zero sets, thus obtaining explicit constants in a result of Levin. The estimates are then used to derive explicit lower bounds for exponential Riesz bases, as they arise in Avdonin's Theorem on 1/4 in the mean or in a Theorem, of Bogmtr, Horvath, Job and Seip. An application is discussed, where knowledge of explicit lower bounds of exponential Riese bases is desirable.
基金supported by Science and Technology Research Project of Jilin Provincial Department of Education of China (Grant No. 2011175)supported by National Natural Science Foundation of China (Grant Nos. 11071250 and 11126149),supported by National Natural Science Foundation of China (Grant Nos. 11071250 and 11271162)Guangdong Provincial Government of China through the "Computational Science Innovative Research Team" program
文摘We characterize a class of piecewise linear spectral sequences. Associated with the spectral sequence, we construct an orthonormal exponential bases for L2（[0,1）d）, which are called generalized Fourier bases. Moreover, we investigate the convergence of Bochner-Riesz means of the generalized Fourier series.
