scholarly journals Oblique Dual Fusion Frames

2018 ◽  
Vol 39 (7) ◽  
pp. 800-824
Author(s):  
Sigrid B. Heineken ◽  
Patricia M. Morillas
Keyword(s):  
Fusion Frames ◽  
Oblique Dual

scholarly journals GENERAL FRAMEWORK FOR CONSISTENT SAMPLING IN HILBERT SPACES

2005 ◽  
Vol 03 (04) ◽  
pp. 497-509 ◽  
Author(s):  
YONINA C. ELDAR ◽  
TOBIAS WERTHER
Keyword(s):  
Hilbert Spaces ◽  
General Framework ◽  
Inner Product ◽  
Riesz Bases ◽  
Oblique Projection ◽  
Dual Frames ◽  
Infinite Dimensional ◽  
Reconstruction Scheme ◽  
Linear Reconstruction ◽  
Oblique Dual

We introduce a general framework for consistent linear reconstruction in infinite-dimensional Hilbert spaces. We study stable reconstructions in terms of Riesz bases and frames, and generalize the notion of oblique dual frames to infinite-dimensional frames. As we show, the linear reconstruction scheme coincides with the so-called oblique projection, which turns into an ordinary orthogonal projection when adapting the inner product. The inner product of interest is, in general, not unique. We characterize the inner products and corresponding positive operators for which the new geometrical interpretation applies.

scholarly journals Weaving K-fusion frames in hilbert spaces

2020 ◽  
Vol 3 (2) ◽  
pp. 101-116
Author(s):  
Hanbing Liu ◽  
◽  
Yongdong Huang ◽  
Chongjun Li ◽  
◽  
...  
Keyword(s):  
Hilbert Spaces ◽  
Fusion Frames

scholarly journals Characterization and Construction of K-Fusion Frames and Their Duals in Hilbert Spaces

2018 ◽  
Vol 73 (1) ◽  
Author(s):  
Fahimeh Arabyani Neyshaburi ◽  
Ali Akbar Arefijamaal
Keyword(s):  
Hilbert Spaces ◽  
Fusion Frames

Fusion Frames for Operators in Hilbert C*-Modules

2020 ◽  
Vol 51 (3) ◽  
pp. 791-803
Author(s):  
M. Khayyami ◽  
A. Nazari
Keyword(s):  
Fusion Frames

scholarly journals GENERAL FRAMEWORK FOR CONSISTENT SAMPLING IN HILBERT SPACES

2005 ◽  
Vol 03 (03) ◽  
pp. 347-359 ◽  
Author(s):  
YONINA C. ELDAR ◽  
TOBIAS WERTHER
Keyword(s):  
Hilbert Spaces ◽  
General Framework ◽  
Inner Product ◽  
Riesz Bases ◽  
Oblique Projection ◽  
Dual Frames ◽  
Infinite Dimensional ◽  
Reconstruction Scheme ◽  
Linear Reconstruction ◽  
Oblique Dual

We introduce a general framework for consistent linear reconstruction in infinite-dimensional Hilbert spaces. We study stable reconstructions in terms of Riesz bases and frames, and generalize the notion of oblique dual frames to infinte-dimensional frames. As we show, the linear reconstruction scheme coincides with the so-called oblique projection, which turns into an ordinary orthogonal projection when adapting the inner product. The inner product of interest is, in general, not unique. We characterize the inner products and the corresponding positive operators for which this geometrical interpretation applies.

Construction of g-fusion frames in Hilbert spaces

2020 ◽  
Vol 23 (02) ◽  
pp. 2050015
Author(s):  
Vahid Sadri ◽  
Gholamreza Rahimlou ◽  
Reza Ahmadi ◽  
Ramazan Zarghami Farfar
Keyword(s):  
Hilbert Spaces ◽  
Closed Range ◽  
Fusion Frames ◽  
Interesting Topic ◽  
Fusion Frame

After introducing g-frames and fusion frames by Sun and Casazza, respectively, combining these frames together is an interesting topic for research. In this paper, we introduce the generalized fusion frames or g-fusion frames for Hilbert spaces and give characterizations of these frames from the viewpoint of closed range and g-fusion frame sequences. Also, the canonical dual g-fusion frames are presented and we introduce a Parseval g-fusion frame.

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