We focus on the L^(p)(R^(2))theory of the fractional Fourier transform(FRFT)for 1≤p≤2.In L^(1)(R^(2)),we mainly study the properties of the FRFT via introducing the two-parameter chirp operator.In order to get the p...We focus on the L^(p)(R^(2))theory of the fractional Fourier transform(FRFT)for 1≤p≤2.In L^(1)(R^(2)),we mainly study the properties of the FRFT via introducing the two-parameter chirp operator.In order to get the pointwise convergence for the inverse FRFT,we introduce the fractional convolution and establish the corresponding approximate identities.Then the well-defined inverse FRFT is given via approximation by suitable means,such as fractional Gauss means and Able means.Furthermore,if the signal F_(α,β)f is received,we give the process of recovering the original signal f with MATLAB.In L^(2)(R^(2)),the general Plancherel theorem,direct sum decomposition,and the general Heisenberg inequality for the FRFT are obtained.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11601427)the China Postdoctoral Science Foundation(No.2017M613193)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2017JQ1009).
文摘We focus on the L^(p)(R^(2))theory of the fractional Fourier transform(FRFT)for 1≤p≤2.In L^(1)(R^(2)),we mainly study the properties of the FRFT via introducing the two-parameter chirp operator.In order to get the pointwise convergence for the inverse FRFT,we introduce the fractional convolution and establish the corresponding approximate identities.Then the well-defined inverse FRFT is given via approximation by suitable means,such as fractional Gauss means and Able means.Furthermore,if the signal F_(α,β)f is received,we give the process of recovering the original signal f with MATLAB.In L^(2)(R^(2)),the general Plancherel theorem,direct sum decomposition,and the general Heisenberg inequality for the FRFT are obtained.
