In this paper, a new distribution space DH is constructed and the definition of the classical Hilbert transform is extended to it. It is shown that DH is the biggest subspace of D on which the extended Hilbert transfo...In this paper, a new distribution space DH is constructed and the definition of the classical Hilbert transform is extended to it. It is shown that DH is the biggest subspace of D on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for Lp functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations of the space DH are given and a class of useful nonlinear phase signals is shown to be in DH. Finally, the applications of the extended Hilbert transform are discussed.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 60475042, 10631080)
文摘In this paper, a new distribution space DH is constructed and the definition of the classical Hilbert transform is extended to it. It is shown that DH is the biggest subspace of D on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for Lp functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations of the space DH are given and a class of useful nonlinear phase signals is shown to be in DH. Finally, the applications of the extended Hilbert transform are discussed.
