Publicação
Multidimensional quadratic-phase Fourier transform and its uncertainty principles
| Resumo: | The main aim of this article is to propose a multidimensional quadratic-phase Fourier transform (MQFT) that generalises the well-known and recently introduced quadratic-phase Fourier transform (as well as, of course, the Fourier transform itself) to higher dimensions. In addition to the definition itself, some crucial properties of this new integral transform will be deduced. These include a Riemann-Lebesgue lemma for the MQFT, a Plancherel lemma for the MQFT and a Hausdorff-Young inequality for the MQFT. A second central objective consists of obtaining different uncertainty principles for this MQFT. To this end, using techniques that include obtaining various auxiliary inequalities, the study culminates in the deduction of Lp-type Heisenberg-Pauli-Weyl uncertainty principles and Lp-type Donoho-Stark uncertainty principles for the MQFT. |
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| Autores principais: | Castro, Luís Pinheiro |
| Outros Autores: | Guerra, Rita Correia |
| Assunto: | Multidimensional quadratic-phase Fourier transform Donoho-Stark uncertainty principle Heisenberg-Pauli-Weyl uncertainty principle Riemann-Lebesgue lemma Hausdorff-Young inequality |
| Ano: | 2025 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Aveiro |
| Idioma: | inglês |
| Origem: | RIA - Repositório Institucional da Universidade de Aveiro |
| Resumo: | The main aim of this article is to propose a multidimensional quadratic-phase Fourier transform (MQFT) that generalises the well-known and recently introduced quadratic-phase Fourier transform (as well as, of course, the Fourier transform itself) to higher dimensions. In addition to the definition itself, some crucial properties of this new integral transform will be deduced. These include a Riemann-Lebesgue lemma for the MQFT, a Plancherel lemma for the MQFT and a Hausdorff-Young inequality for the MQFT. A second central objective consists of obtaining different uncertainty principles for this MQFT. To this end, using techniques that include obtaining various auxiliary inequalities, the study culminates in the deduction of Lp-type Heisenberg-Pauli-Weyl uncertainty principles and Lp-type Donoho-Stark uncertainty principles for the MQFT. |
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