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On approximate support versions of Donoho--Stark uncertainty principles for k-Hadamard operators

  • Rami Ayoush
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Abstract

In this paper we present results related to Donoho--Stark type uncertainty principles that were proved in the article "The uncertainty principle: variations on a theme" by Wigderson and Wigderson for k-Hadamard operators in the finite-dimensional setting. Namely, the authors showed that Donoho-Stark principles can be generalized to versions for approximate supports with respect to norms ℓp for p=1 and p=2. In the second case they assumed the so-called speciality condition, namely that a suitable matrix satisfies A*A = kI. First we show that such theorems cannot be generalized to p>1 if matrices are not special k-Hadamard. Next we prove Donoho-Stark type principle for special k-Hadamard operators for ℓp norms within the range 1≤ p≤ 2. Finally, we show that such theorems are false for p>2 even in the presence of the speciality condition.

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Cite

BibTeXRIS
BibTeX
@misc{ayoush2026approximate,
  title = {{On approximate support versions of Donoho--Stark uncertainty principles for $k$-Hadamard operators}},
  author = {Rami Ayoush},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41902},
  eprint = {2610.41902},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41902},
}
RIS
TY  - UNPB
TI  - On approximate support versions of Donoho--Stark uncertainty principles for k-Hadamard operators
AU  - Rami Ayoush
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41902
UR  - https://arxiv.org/abs/2610.41902
AB  - In this paper we present results related to Donoho--Stark type uncertainty principles that were proved in the article "The uncertainty principle: variations on a theme" by Wigderson and Wigderson for k-Hadamard operators in the finite-dimensional setting. Namely, the authors showed that Donoho-Stark principles can be generalized to versions for approximate supports with respect to norms ℓ^p for p=1 and p=2. In the second case they assumed the so-called speciality condition, namely that a suitable matrix satisfies A^*A = kI. First we show that such theorems cannot be generalized to p>1 if matrices are not special k-Hadamard. Next we prove Donoho-Stark type principle for special k-Hadamard operators for ℓ^p norms within the range 1≤ p≤ 2. Finally, we show that such theorems are false for p>2 even in the presence of the speciality condition.
ER  -