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On the local integrability condition for generalised translation-invariant systems

(2019) COLLECTANEA MATHEMATICA. 70(3). p.407-429
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Abstract
This paper considers the local integrability condition for generalised translation-invariant systems and its relation to the Calderon integrability condition, the temperateness condition and the uniform counting estimate. It is shown that sufficient and necessary conditions for satisfying the local integrability condition are closely related to lower and upper bounds on the number of lattice points that intersect with the translates of a compact set. The results are complemented by examples that illustrate the crucial interplay between the translation subgroups and the generating functions of the system.
Keywords
Applied Mathematics, General Mathematics, Calderon integrability condition, Frames, Generalised translation-invariant systems, Local integrability condition, Uniform counting estimate, FRAMES, SPACES

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MLA
Van Velthoven, Jordy. “On the Local Integrability Condition for Generalised Translation-Invariant Systems.” COLLECTANEA MATHEMATICA, vol. 70, no. 3, 2019, pp. 407–29, doi:10.1007/s13348-019-00238-5.
APA
Van Velthoven, J. (2019). On the local integrability condition for generalised translation-invariant systems. COLLECTANEA MATHEMATICA, 70(3), 407–429. https://doi.org/10.1007/s13348-019-00238-5
Chicago author-date
Van Velthoven, Jordy. 2019. “On the Local Integrability Condition for Generalised Translation-Invariant Systems.” COLLECTANEA MATHEMATICA 70 (3): 407–29. https://doi.org/10.1007/s13348-019-00238-5.
Chicago author-date (all authors)
Van Velthoven, Jordy. 2019. “On the Local Integrability Condition for Generalised Translation-Invariant Systems.” COLLECTANEA MATHEMATICA 70 (3): 407–429. doi:10.1007/s13348-019-00238-5.
Vancouver
1.
Van Velthoven J. On the local integrability condition for generalised translation-invariant systems. COLLECTANEA MATHEMATICA. 2019;70(3):407–29.
IEEE
[1]
J. Van Velthoven, “On the local integrability condition for generalised translation-invariant systems,” COLLECTANEA MATHEMATICA, vol. 70, no. 3, pp. 407–429, 2019.
@article{8708893,
  abstract     = {{This paper considers the local integrability condition for generalised translation-invariant systems and its relation to the Calderon integrability condition, the temperateness condition and the uniform counting estimate. It is shown that sufficient and necessary conditions for satisfying the local integrability condition are closely related to lower and upper bounds on the number of lattice points that intersect with the translates of a compact set. The results are complemented by examples that illustrate the crucial interplay between the translation subgroups and the generating functions of the system.}},
  author       = {{Van Velthoven, Jordy}},
  issn         = {{0010-0757}},
  journal      = {{COLLECTANEA MATHEMATICA}},
  keywords     = {{Applied Mathematics,General Mathematics,Calderon integrability condition,Frames,Generalised translation-invariant systems,Local integrability condition,Uniform counting estimate,FRAMES,SPACES}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{407--429}},
  title        = {{On the local integrability condition for generalised translation-invariant systems}},
  url          = {{http://dx.doi.org/10.1007/s13348-019-00238-5}},
  volume       = {{70}},
  year         = {{2019}},
}

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