Donoho–Stark and Price uncertainty principles for a class of q-integral transforms with bounded kernels
-
Luis P. Castro
and
Rita C. Guerra
Abstract
We consider a very global q-integral transform, essentially characterized by having a bounded kernel and satisfying a set of natural and useful properties for the realization of applications. The main ambition of this work is to seek conditions that guarantee uncertainty principles of the Donoho–Stark type for that class of q-integral transforms. It should be noted that the global character of the q-integral transform in question allows one to immediately deduce corresponding Donoho–Stark uncertainty principles for q-integral operators that are its particular cases. These particular cases are very well-known operators, namely: a q-cosine-Fourier transform, a q-sine-Fourier transform, a q-Fourier transform, a q-Bessel–Fourier transform and a q-Dunkl transform. Moreover, generalizations of the local uncertainty principle of Price for the q-cosine-Fourier transform, q-sine-Fourier transform, q-Fourier transform, q-Bessel–Fourier transform and q-Dunkl transform are also obtained.
Award Identifier / Grant number: UIDB/04106/2020
Award Identifier / Grant number: UIDP/00324/2020
Funding statement: Luis P. Castro and Rita C. Guerra were supported in part by FCT–Portuguese Foundation for Science and Technology through the Center for Research and Development in Mathematics and Applications (CIDMA) of Universidade de Aveiro, within project UIDB/04106/2020. Rita C. Guerra was also supported, for part of the time, by the Centre for Mathematics of the University of Coimbra (CMUC) – UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES, and also acknowledges a postdoctoral research fellowship supported by CMUC – UIDP/00324/2020.
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Articles in the same Issue
- Frontmatter
- A note on the essential numerical range of block diagonal operators
- Tilings of the sphere by congruent quadrilaterals III: Edge combination a 3 b with general angles
- Schauder estimates for Bessel operators
- Spectral invariance of quasi-Banach algebras of matrices and pseudodifferential operators
- Multiple normalized solutions for fractional elliptic problems
- L-series of weakly holomorphic quasimodular forms and a converse theorem
- Supercongruences arising from a 7 F 6 hypergeometric transformation formula
- Sharp Sobolev and Adams–Trudinger–Moser embeddings on weighted Sobolev spaces and their applications
- On the modular isomorphism problem for groups of nilpotency class 2 with cyclic center
- The quotient set of the quadratic distance set over finite fields
- Donoho–Stark and Price uncertainty principles for a class of q-integral transforms with bounded kernels
- Improved spectral cluster bounds for orthonormal systems
- Multilinear Fourier integral operators on modulation spaces
- One-sided Gorenstein rings
- Multilinear fourier integral operators on modulation spaces
Articles in the same Issue
- Frontmatter
- A note on the essential numerical range of block diagonal operators
- Tilings of the sphere by congruent quadrilaterals III: Edge combination a 3 b with general angles
- Schauder estimates for Bessel operators
- Spectral invariance of quasi-Banach algebras of matrices and pseudodifferential operators
- Multiple normalized solutions for fractional elliptic problems
- L-series of weakly holomorphic quasimodular forms and a converse theorem
- Supercongruences arising from a 7 F 6 hypergeometric transformation formula
- Sharp Sobolev and Adams–Trudinger–Moser embeddings on weighted Sobolev spaces and their applications
- On the modular isomorphism problem for groups of nilpotency class 2 with cyclic center
- The quotient set of the quadratic distance set over finite fields
- Donoho–Stark and Price uncertainty principles for a class of q-integral transforms with bounded kernels
- Improved spectral cluster bounds for orthonormal systems
- Multilinear Fourier integral operators on modulation spaces
- One-sided Gorenstein rings
- Multilinear fourier integral operators on modulation spaces
