• Corpus ID: 239024569

# Approximately Dual p-Approximate Schauder Frames

@inproceedings{Krishna2021ApproximatelyDP,
title={Approximately Dual p-Approximate Schauder Frames},
author={K. Mahesh Krishna and P. S. Johnson},
year={2021}
}
• Published 19 October 2021
• Mathematics
Abstract. Difficulty in the construction of dual frames for a given Hilbert space led to the introduction of approximately dual frames in Hilbert spaces by Christensen and Laugesen. It becomes even more difficult in Banach spaces to construct duals. For this purpose, we introduce approximately dual frames for a class of approximate Schauder frames for Banach spaces and develop basic theory. Approximate duals for this subclass is completely characterized and its perturbation is also studied.
3 Citations
Feichtinger Conjectures, $R_\varepsilon$-Conjectures and Weaver's Conjectures for Banach spaces
Abstract: Motivated from two decades old famous Feichtinger conjectures for frames, Rε-conjecture and Weaver’s conjecture for Hilbert spaces (and their solution by Marcus, Spielman, and Srivastava),
Operator-Valued p-Approximate Schauder Frames
• Mathematics
• 2022
X iv :2 20 1. 03 95 5v 1 [ m at h. FA ] 1 0 Ja n 20 22 OPERATOR-VALUED p-APPROXIMATE SCHAUDER FRAMES K. MAHESH KRISHNA Statistics and Mathematics Unit Indian Statistical Institute, Bangalore Centre
The $(abc,pqr)$-problem for Approximate Schauder Frames for Banach Spaces
(abc, pqr)-problem for approximate Schauder frames for Banach spaces L(R), 1 < p < ∞ is formulated.

## References

SHOWING 1-10 OF 24 REFERENCES
Towards characterizations of approximate Schauder frame and its duals for Banach spaces
• Mathematics
• 2020
Characterizations for a frame and its duals are known for separable Hilbert spaces. In this paper, we characterize a class of approximate Schauder frame and its duals for separable Banach spaces. We
Pre-frame operators, Besselian frames, and near-Riesz bases in Hilbert spaces
A problem of enduring interest in connection with the study of frames in Hilbert space is that of characterizing those frames which can essentially be regarded as Riesz bases for computational
Approximately dual frames in Hilbert spaces and applications to Gabor frames
• Mathematics
• 2011
Approximately dual frames are studied in the Hilbert space setting. Approximate duals are easier to construct than classical dual frames, and can be tailored to yield almost perfect reconstruction.
On excesses of frames
• Mathematics
• 2015
We show that any two frames in a separable Hilbert space that are dual to each other have the same excess. Some new relations for the analysis resp. synthesis operators of dual frames are also
Generalized shift-invariant systems and approximately dual frames
• Mathematics
• 2017
Dual pairs of frames yield a procedure for obtaining perfect reconstruction of elements in the underlying Hilbert space in terms of superpositions of the frame elements. However, practical
Wavelets in Littlewood–Paley space, and Mexican hat completeness
• Mathematics
• 2011
Abstract We resolve a long-standing question on completeness of the non-orthogonal Mexican hat wavelet system, in L p for 1 p 2 and in the Hardy space H p for 2 / 3 p ⩽ 1 . Tools include the discrete
On general frame decompositions
We provide a characterization and construction of general frame decompositions. We show that generating all duals for a given frame amounts to finding left inverses of an one-to-one mapping. A
Deficits and Excesses of Frames
• Mathematics, Computer Science