Linear independence of time–frequency translates in Lp spaces
We study the Heil–Ramanathan–Topiwala conjecture in Lp spaces by reformulating it as a fixed point problem. This reformulation shows that a function with linearly dependent time–frequency translates has a very rigid structure, which is encoded in a family of linear operators. This is used to give an...
Guardado en:
| Autores principales: | , , |
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| Formato: | Articulo Contribucion a revista |
| Lenguaje: | Inglés |
| Publicado: |
2020
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/138133 |
| Aporte de: |
| id |
I19-R120-10915-138133 |
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| record_format |
dspace |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Matemática Time frequency translates Linear independence Ergodicity Symplectic transformation Lattice Lp spaces |
| spellingShingle |
Matemática Time frequency translates Linear independence Ergodicity Symplectic transformation Lattice Lp spaces Antezana, Jorge Abel Bruna, Joaquim Pujals, Enrique Linear independence of time–frequency translates in Lp spaces |
| topic_facet |
Matemática Time frequency translates Linear independence Ergodicity Symplectic transformation Lattice Lp spaces |
| description |
We study the Heil–Ramanathan–Topiwala conjecture in Lp spaces by reformulating it as a fixed point problem. This reformulation shows that a function with linearly dependent time–frequency translates has a very rigid structure, which is encoded in a family of linear operators. This is used to give an elementary proof that if f∈Lp(R), p∈[1,2], and Λ⊆R×R is contained in a lattice then the set of time frequency translates (f(a,b))(a,b)∈Λ is linearly independent. Our proof also works for the case 2 < p < ∞ if Λ is contained in a lattice of the form αZ×βZ. |
| format |
Articulo Contribucion a revista |
| author |
Antezana, Jorge Abel Bruna, Joaquim Pujals, Enrique |
| author_facet |
Antezana, Jorge Abel Bruna, Joaquim Pujals, Enrique |
| author_sort |
Antezana, Jorge Abel |
| title |
Linear independence of time–frequency translates in Lp spaces |
| title_short |
Linear independence of time–frequency translates in Lp spaces |
| title_full |
Linear independence of time–frequency translates in Lp spaces |
| title_fullStr |
Linear independence of time–frequency translates in Lp spaces |
| title_full_unstemmed |
Linear independence of time–frequency translates in Lp spaces |
| title_sort |
linear independence of time–frequency translates in lp spaces |
| publishDate |
2020 |
| url |
http://sedici.unlp.edu.ar/handle/10915/138133 |
| work_keys_str_mv |
AT antezanajorgeabel linearindependenceoftimefrequencytranslatesinlpspaces AT brunajoaquim linearindependenceoftimefrequencytranslatesinlpspaces AT pujalsenrique linearindependenceoftimefrequencytranslatesinlpspaces |
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Repositorios |
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1764820456771158017 |