scholarly journals The effect of perturbations of frames on their alternate and approximately dual frames

2021 ◽  
Author(s):  
Hossein Javanshiri ◽  
Mahin Hajiabootorabi ◽  
Mohammad R. Mardanbeigi
Keyword(s):  
Dual Frames

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.

A Z-Axis Decoupled Micromachined Gyroscope with Dual Frames

2011 ◽  
Vol 483 ◽  
pp. 169-173
Author(s):  
Hai Lin Tang ◽  
Xian Xue Liu ◽  
Hao Zhou
Keyword(s):  
Quality Factor ◽  
Test Results ◽  
Dual Frames ◽  
Fabrication Errors ◽  
Micromachined Gyroscope

A z-axis decoupled micromachined gyroscope with dual frames is designed, fabricated and tested. The robust structure considering fabrication errors is obtained by the use of optimal robustness of design and process compensation. The gyroscope is packaged in vacuum, and test results show that quality factor of driving and sensing modes are 2000 and 800, respectively. In the range of 0~2400 deg/sec, sensitivity and linearity of the fabricated gyroscope are 1 deg/sec and 0.3%, respectively.

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.

scholarly journals Sums of A Pair of Orthogonal Frames

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 582
Author(s):  
Ghanshyam Bhatt
Keyword(s):  
Linear Operator ◽  
Bounded Linear Operator ◽  
Sufficient Condition ◽  
Simple Construction ◽  
Necessary And Sufficient Condition ◽  
Dual Frames ◽  
Bounded Linear ◽  
Frame Bounds ◽  
Necessary And Sufficient

Frames are more stable as compared to bases under the action of a bounded linear operator. Sums of different frames under the action of a bounded linear operator are studied with the help of analysis, synthesis and frame operators. A simple construction of frames from the existing ones under the action of such an operator is presented here. It is shown that a frame can be added to its alternate dual frames, yielding a new frame. It is also shown that the sum of a pair of orthogonal frames is a frame. This provides an easy construction of a frame where the frame bounds can be computed easily. Moreover, for a pair of orthogonal frames, the necessary and sufficient condition is presented for their alternate dual frames to be orthogonal. This allows for an easy construction of a large number of new frames.

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