A space Df is constructed and some characterizations of space Df are given. It is shown that the classical Fourier transform is extended to the distribution space Df, which can be embedded into the Schwartz distribution space D＇ continuously. It is also shown that D＇f is the biggest embedded subspace of D on which the extended Fourier transform, f, is a homeomorphism of D＇f onto itself.
In this paper, a new distribution space is constructed and the definition of the classical Hilbert transform is extended to it. It is shown that is the biggest subspace of on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for L p functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations of the space are given and a class of useful nonlinear phase signals is shown to be in . Finally, the applications of the extended Hilbert transform are discussed.
YANG LiHua School of Mathematics and Computing Science, Sun Yat-Sen University, Guangzhou 510275, China
More than 8.2 million effective data samples were obtained by the Chang’E-1 Laser Altimeter (LAM).In order to produce a global topographic model of the moon with improved accuracy,a hierarchical many-knot spline method was proposed in this paper.This algorithm makes use of a hierarchy of control lattices to approximate or interpolate the LAM data.Based on the proposed algorithm,a 0.0625°×0.0625° grid of global lunar DEM was obtained and it was compared with ULCN2005,CLTMs01 and Kaguya models,respectively.At the same time,this paper explored the elevation distribution law and established the elevation distribution model.It is shown that the global lunar and nearside elevation distribution is positively skewed and leptokurtic normal distribution,and the farside elevation distribution is a positively skewed and platykurtic normal distribution.
CAI ZhanChuan1,2,ZHENG CaiMu1,2,TANG ZeSheng1,2,3 & QI DongXu1,2,4 1 Faculty of Information Technology,Macao University of Science and Technology,Macao,China
In this paper, we investigate the simultaneous approximation of Bernstein- Sikkema operators, and establish the direct and equivalent theorems by using the Ditzian-Totik modulus of smoothness.
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.
