Motivated by representing multidimensional periodic nonlinear and non-stationary signals （functions）, we study a class of orthonormal exponential basis for L2（Id） with I ：= [0, 1）, whose exponential parts are pi...Motivated by representing multidimensional periodic nonlinear and non-stationary signals （functions）, we study a class of orthonormal exponential basis for L2（Id） with I ：= [0, 1）, whose exponential parts are piecewise linear spectral sequences with p-knots. It is widely applied in time-frequency analysis.展开更多
We investigate two classes of orthonormal bases for L^2（[0, 1）^n）. The exponential parts of those bases are multi-knot piecewise linear functions which are called spectral sequences. We characterize the multi-knot ...We investigate two classes of orthonormal bases for L^2（[0, 1）^n）. The exponential parts of those bases are multi-knot piecewise linear functions which are called spectral sequences. We characterize the multi-knot piecewise linear spectral sequences and give an application of the first class of piecewise linear spectral sequences.展开更多
Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,...Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,0)^(t),(1,0)^(t),(0,1)^(t)}is the Sierpinski digit.We prove that there exists a setΛ⊂ℝ2 such that the family{e2πi〈λ,x〉:λ∈Λ} is an orthonormal basis of L^(2)(μ{A_(n),n≥1})if and only if 1/3(1,-1)A_(n)∈Z^(2)for n≥2 under some metric conditions on A_(n).展开更多
基金Supported in part by the President Fund of GUCASSupported in part by National Natural Foundation of China(Grant No.10631080)National Natural Foundation of Beijing (Grant No.1092004)
文摘Motivated by representing multidimensional periodic nonlinear and non-stationary signals （functions）, we study a class of orthonormal exponential basis for L2（Id） with I ：= [0, 1）, whose exponential parts are piecewise linear spectral sequences with p-knots. It is widely applied in time-frequency analysis.
基金Supported in part by National Natural Science Foundation of China (Grant No.10631080)Natural Science Foundation of Beijing (Grant No.1092004)
文摘We investigate two classes of orthonormal bases for L^2（[0, 1）^n）. The exponential parts of those bases are multi-knot piecewise linear functions which are called spectral sequences. We characterize the multi-knot piecewise linear spectral sequences and give an application of the first class of piecewise linear spectral sequences.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12371087, 11971109,11971194, 11672074 and 12271185)supported by the program for Probability and Statistics:Theory and Application (Grant No. IRTL1704)+1 种基金the program for Innovative Research Team in Science and Technology in Fujian Province University (Grant No. IRTSTFJ)supported by Guangdong NSFC (Grant No. 2022A1515011124)
文摘Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,0)^(t),(1,0)^(t),(0,1)^(t)}is the Sierpinski digit.We prove that there exists a setΛ⊂ℝ2 such that the family{e2πi〈λ,x〉:λ∈Λ} is an orthonormal basis of L^(2)(μ{A_(n),n≥1})if and only if 1/3(1,-1)A_(n)∈Z^(2)for n≥2 under some metric conditions on A_(n).
