Let г^＋ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г＋ as endomorphisms of C^＊-algebras, and use this to generalize the t...Let г^＋ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г＋ as endomorphisms of C^＊-algebras, and use this to generalize the theorem of Ji.展开更多
We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform （CWFT）. Based on the spectral representation of the Clifford Fourier transform （...We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform （CWFT）. Based on the spectral representation of the Clifford Fourier transform （CFT）, we derive several important properties such as shift, modulation, reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to show the differences between the classical windowed Fourier transform （WFT） and the CWFT. Finally, as an application we establish a Heisenberg type uncertainty principle for the CWFT.展开更多
基金the Academy of Sciences of Malaysia through SAGA Projectthe Indonesian Research Fund for Doctorate Sandwich Programs(URGE)
文摘Let г^＋ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г＋ as endomorphisms of C^＊-algebras, and use this to generalize the theorem of Ji.
文摘We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform （CWFT）. Based on the spectral representation of the Clifford Fourier transform （CFT）, we derive several important properties such as shift, modulation, reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to show the differences between the classical windowed Fourier transform （WFT） and the CWFT. Finally, as an application we establish a Heisenberg type uncertainty principle for the CWFT.
