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φ-FRAMES AND φ-RIESZ BASES ON LOCALLY COMPACT ABELIAN GROUPS
Gol, Rajab Ali Kamyabi,Tousi, Reihaneh Raisi Korean Mathematical Society 2011 대한수학회지 Vol.48 No.5
We introduce ${\varphi}$-frames in $L^2$(G), as a generalization of a-frames defined in [8], where G is a locally compact Abelian group and ${\varphi}$ is a topological automorphism on G. We give a characterization of ${\varphi}$-frames with regard to usual frames in $L^2$(G) and show that ${\varphi}$-frames share several useful properties with frames. We define the associated ${\varphi}$-analysis and ${\varphi}$-preframe operators, with which we obtain criteria for a sequence to be a ${\varphi}$-frame or a ${\varphi}$-Bessel sequence. We also define ${\varphi}$-Riesz bases in $L^2$(G) and establish equivalent conditions for a sequence in $L^2$(G) to be a ${\varphi}$-Riesz basis.
φ-FRAMES AND φ-RIESZ BASES ON LOCALLY COMPACT ABELIAN GROUPS
Rajab Ali Kamyabi Gol,Reihaneh Raisi Tousi 대한수학회 2011 대한수학회지 Vol.48 No.5
We introduce φ-frames in L^2(G), as a generalization of a-frames dened in [8], where G is a locally compact Abelian group and φ is a topological automorphism on G. We give a characterization of φ-frames with regard to usual frames in L^2(G) and show that φ-frames share several useful properties with frames. We dene the associated φ-analysis and φ-preframe operators, with which we obtain criteria for a sequence to be a φ-frame or a φ-Bessel sequence. We also define φ-Riesz bases in L^2(G) and establish equivalent conditions for a sequence in L^2(G) to be a φ-Riesz basis.
DISTANCE BETWEEN CONTINUOUS FRAMES IN HILBERT SPACE
Amiri, Zahra,Kamyabi-Gol, Rajab Ali Korean Mathematical Society 2017 대한수학회지 Vol.54 No.1
In this paper, we study some equivalence relations between continuous frames in a Hilbert space ${\mathcal{H}}$. In particular, we seek two necessary and sufficient conditions under which two continuous frames are near. Moreover, we investigate a distance between continuous frames in order to acquire the closest and nearest tight continuous frame to a given continuous frame. Finally, we implement these results for shearlet and wavelet frames in two examples.
DISTANCE BETWEEN CONTINUOUS FRAMES IN HILBERT SPACE
Zahra Amiri,Rajab Ali Kamyabi Gol 대한수학회 2017 대한수학회지 Vol.54 No.1
In this paper, we study some equivalence relations between continuous frames in a Hilbert space $\mathcal{H}$. In particular, we seek two necessary and sufficient conditions under which two continuous frames are near. Moreover, we investigate a distance between continuous frames in order to acquire the closest and nearest tight continuous frame to a given continuous frame. Finally, we implement these results for shearlet and wavelet frames in two examples.
Sharpening lower bound in some inequalities for frames in Hilbert spaces
Fahimeh Sultanzadeh,Mahmood Hassani,Mohsen Erfanian Omidvar,Rajab Ali Kamyabi Gol 강원경기수학회 2021 한국수학논문집 Vol.29 No.4
This paper aims to present a new lower bound for some inequalities related to Frames in Hilbert space. Some refinements of the inequalities for general frames and alternate dual frames under suitable conditions are given. These results refine the remarkable results obtained by Balan et al. and Gavruta.