Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable ...Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable conditions which imply that the wavelet systems are wavelet frames is among the core problems in time-frequency analysis. In this article, we establish some new inequalities for wavelet frames on local fields of positive characteristic by means of the Fourier transform. As an application, an improved version of the Li-Jiang inequality for wavelet frames on local fields is obtained.展开更多
In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of po...In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic.展开更多
In this article,we introduce the notion of general multiresolution structure(GMS)in the reducing subspace over local fields.We show that the GMS is admitted by an arbitrary reducing subspace and characterize all those...In this article,we introduce the notion of general multiresolution structure(GMS)in the reducing subspace over local fields.We show that the GMS is admitted by an arbitrary reducing subspace and characterize all those GMSs which admit a pyramids decomposition.Towards the culmination,we obtain a frame-like expansion for signals in reducing subspaces in terms of GMS over local fields.展开更多
基金supported by NBHM, Department of Atomic Energy, Government of India (Grant No. 2/48(8)/2016/NBHM(R.P)/R&D II/13924)
文摘Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable conditions which imply that the wavelet systems are wavelet frames is among the core problems in time-frequency analysis. In this article, we establish some new inequalities for wavelet frames on local fields of positive characteristic by means of the Fourier transform. As an application, an improved version of the Li-Jiang inequality for wavelet frames on local fields is obtained.
文摘In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic.
文摘In this article,we introduce the notion of general multiresolution structure(GMS)in the reducing subspace over local fields.We show that the GMS is admitted by an arbitrary reducing subspace and characterize all those GMSs which admit a pyramids decomposition.Towards the culmination,we obtain a frame-like expansion for signals in reducing subspaces in terms of GMS over local fields.
