Let A be a d x d real expansive matrix. An A-dilation Parseval frame wavelet is a function φ E n2 （Rd）, such that the set {｜det A｜n/2φ（Ant -l） ：n ∈ Z, l∈ Zd} forms a Parseval frame for L2 （Rd）. A measurab...Let A be a d x d real expansive matrix. An A-dilation Parseval frame wavelet is a function φ E n2 （Rd）, such that the set {｜det A｜n/2φ（Ant -l） ：n ∈ Z, l∈ Zd} forms a Parseval frame for L2 （Rd）. A measurable function f is called an A-dilation Parseval frame wavelet multiplier if the inverse Fourier transform of fφ is an A-dilation Parseval frame wavelet whenever φ is an A-dilation Parseval frame wavelet, where φ denotes the Fourier transform of φ. In this paper, the authors completely characterize all A-dilation Parseval frame wavelet multipliers for any integral expansive matrix A with ｜ det（A）｜= 2. As an application, the path-connectivity of the set of all A-dilation Parseval frame wavelets with a frame MRA in L2（Rd） is discussed.展开更多
Suppose that η1,...,η_n are measurable functions in L2（R）.We call the n-tuple（η1,...,ηn） a Parseval super frame wavelet of length n if {2^（k/2） η1（2~kt-l） ⊕···⊕2^（k/2） ηn（2kt-l）：k,l...Suppose that η1,...,η_n are measurable functions in L2（R）.We call the n-tuple（η1,...,ηn） a Parseval super frame wavelet of length n if {2^（k/2） η1（2~kt-l） ⊕···⊕2^（k/2） ηn（2kt-l）：k,l∈Z} is a Parseval frame for L2（R）⊕n.In high dimensional case,there exists a similar notion of Parseval super frame wavelet with some expansive dilation matrix.In this paper,we will study the Parseval super frame wavelets of length n,and will focus on the path-connectedness of the set of all s-elementary Parseval super frame wavelets in one-dimensional and high dimensional cases.We will prove the corresponding path-connectedness theorems.展开更多
In this paper,we characterize all generalized low pass filters and MRA Parseval frame wavelets in L 2 （R n ） with matrix dilations of the form （Df）（x） =√ 2f（Ax）,where A is an arbitrary expanding n × n ma...In this paper,we characterize all generalized low pass filters and MRA Parseval frame wavelets in L 2 （R n ） with matrix dilations of the form （Df）（x） =√ 2f（Ax）,where A is an arbitrary expanding n × n matrix with integer coefficients,such that ｜det A｜ = 2.We study the pseudo-scaling functions,generalized low pass filters and MRA Parseval frame wavelets and give some important characterizations about them.Furthermore,we give a characterization of the semiorthogonal MRA Parseval frame wavelets and provide several examples to verify our results.展开更多
We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds. We characterize those operators that produces Parseval controlled frames also we state a way to construct nea...We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds. We characterize those operators that produces Parseval controlled frames also we state a way to construct nearly Parseval controlled frames. We intro- duce a new perturbation of controlled frames to obtain new frames from a given one. Also we reduce the distance of frames by appropriate operators and produce nearly dual frames from two given frames which are not dual frames for each other.展开更多
In this paper, we give a method which aUows us to construct a class of Parseval frames for L2（R） from Fourier frame for L2（X）. The result shows that the function which generates a Oabor frame by translations and m...In this paper, we give a method which aUows us to construct a class of Parseval frames for L2（R） from Fourier frame for L2（X）. The result shows that the function which generates a Oabor frame by translations and modulations has ＂good＂ properties, i.e., it is suifficiently smooth and compactly supported.展开更多
Regarding the application of the fusion frames and generalization of them in data proceeding,their iterative is of particular importance when one of their members is deleted.In this note,a method for reconstruction of...Regarding the application of the fusion frames and generalization of them in data proceeding,their iterative is of particular importance when one of their members is deleted.In this note,a method for reconstruction of generalized fusion frames and error operator with its upper bound are presented.Also,the approximation operator for these frames will be introduced and we study some results about them.展开更多
In this paper we discuss about c-frames, namely continuous frames. Since, cframes are generalizations of discrete frames, we generalize some results of discrete frames to continuous version. We explain some results ab...In this paper we discuss about c-frames, namely continuous frames. Since, cframes are generalizations of discrete frames, we generalize some results of discrete frames to continuous version. We explain some results about relations of projections in Hilbert spaces and c-frames to characterize these frames. Also, we will specify（precisely） the synthesis and frame operators of Bochner integrable c-frames. Finally, we classify Hilbert-Schmidt operators by c-frames and express some new identities for Parseval c-frames.展开更多
基金Project Supported by the National Natural Science Foundation of China(Nos.11071065,11101142,11171306,10671062)the China Postdoctoral Science Foundation(No.20100480942)+1 种基金the Doctoral Program Foundation of the Ministry of Education of China(No.20094306110004) the Program for Science and Technology Research Team in Higher Educational Institutions of Hunan Province
文摘Let A be a d x d real expansive matrix. An A-dilation Parseval frame wavelet is a function φ E n2 （Rd）, such that the set {｜det A｜n/2φ（Ant -l） ：n ∈ Z, l∈ Zd} forms a Parseval frame for L2 （Rd）. A measurable function f is called an A-dilation Parseval frame wavelet multiplier if the inverse Fourier transform of fφ is an A-dilation Parseval frame wavelet whenever φ is an A-dilation Parseval frame wavelet, where φ denotes the Fourier transform of φ. In this paper, the authors completely characterize all A-dilation Parseval frame wavelet multipliers for any integral expansive matrix A with ｜ det（A）｜= 2. As an application, the path-connectivity of the set of all A-dilation Parseval frame wavelets with a frame MRA in L2（Rd） is discussed.
基金Supported by the National Natural Science Foundation of China(11071065,11101142,11171306,10671062)the China Postdoctoral Science Foundation(20100480942)+1 种基金the Ph.D.Programs Foundation of the Ministry of Education of China(20094306110004)the Program for Science and Technology Research Team in Higher Educational Institutions of Hunan Province
文摘Suppose that η1,...,η_n are measurable functions in L2（R）.We call the n-tuple（η1,...,ηn） a Parseval super frame wavelet of length n if {2^（k/2） η1（2~kt-l） ⊕···⊕2^（k/2） ηn（2kt-l）：k,l∈Z} is a Parseval frame for L2（R）⊕n.In high dimensional case,there exists a similar notion of Parseval super frame wavelet with some expansive dilation matrix.In this paper,we will study the Parseval super frame wavelets of length n,and will focus on the path-connectedness of the set of all s-elementary Parseval super frame wavelets in one-dimensional and high dimensional cases.We will prove the corresponding path-connectedness theorems.
基金Supported by the National Natural Science Foundation of China (Grant No. 60774041)the Natural Science Foundation for the Education Department of Henan Province of China (Grant No. 2010A110002)
文摘In this paper,we characterize all generalized low pass filters and MRA Parseval frame wavelets in L 2 （R n ） with matrix dilations of the form （Df）（x） =√ 2f（Ax）,where A is an arbitrary expanding n × n matrix with integer coefficients,such that ｜det A｜ = 2.We study the pseudo-scaling functions,generalized low pass filters and MRA Parseval frame wavelets and give some important characterizations about them.Furthermore,we give a characterization of the semiorthogonal MRA Parseval frame wavelets and provide several examples to verify our results.
文摘We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds. We characterize those operators that produces Parseval controlled frames also we state a way to construct nearly Parseval controlled frames. We intro- duce a new perturbation of controlled frames to obtain new frames from a given one. Also we reduce the distance of frames by appropriate operators and produce nearly dual frames from two given frames which are not dual frames for each other.
基金Supported by Henan Province Education Department Natural Science Foundation of China（2008B510001）
文摘In this paper, we give a method which aUows us to construct a class of Parseval frames for L2（R） from Fourier frame for L2（X）. The result shows that the function which generates a Oabor frame by translations and modulations has ＂good＂ properties, i.e., it is suifficiently smooth and compactly supported.
文摘Regarding the application of the fusion frames and generalization of them in data proceeding,their iterative is of particular importance when one of their members is deleted.In this note,a method for reconstruction of generalized fusion frames and error operator with its upper bound are presented.Also,the approximation operator for these frames will be introduced and we study some results about them.
文摘In this paper we discuss about c-frames, namely continuous frames. Since, cframes are generalizations of discrete frames, we generalize some results of discrete frames to continuous version. We explain some results about relations of projections in Hilbert spaces and c-frames to characterize these frames. Also, we will specify（precisely） the synthesis and frame operators of Bochner integrable c-frames. Finally, we classify Hilbert-Schmidt operators by c-frames and express some new identities for Parseval c-frames.
