Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity
Journal of Geometric Analysis, ISSN: 1050-6926, Vol: 25, Issue: 1, Page: 226-254
2015
- 6Citations
- 8Usage
- 8Captures
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Metrics Details
- Citations6
- Citation Indexes6
- CrossRef4
- Usage8
- Abstract Views8
- Captures8
- Readers8
Article Description
We prove that the HRT (Heil, Ramanathan, and Topiwala) conjecture holds for finite Gabor systems generated by square-integrable functions with certain behavior at infinity. These functions include functions ultimately decaying faster than any exponential function, as well as square-integrable functions ultimately analytic and whose germs are in a Hardy field that is closed under translations. Two classes of the latter type of functions are the set of square-integrable logarithmico-exponential functions and the set of square-integrable Pfaffian functions. We also prove the HRT conjecture for certain finite Gabor systems generated by positive functions.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84878727802&origin=inward; http://dx.doi.org/10.1007/s12220-013-9423-8; http://link.springer.com/10.1007/s12220-013-9423-8; http://link.springer.com/content/pdf/10.1007/s12220-013-9423-8; http://link.springer.com/content/pdf/10.1007/s12220-013-9423-8.pdf; http://link.springer.com/article/10.1007/s12220-013-9423-8/fulltext.html; https://nsuworks.nova.edu/math_facarticles/70; https://nsuworks.nova.edu/cgi/viewcontent.cgi?article=1069&context=math_facarticles; https://dx.doi.org/10.1007/s12220-013-9423-8; https://link.springer.com/article/10.1007/s12220-013-9423-8
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