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2 results

  • TWISTED SHIFT-INVARIANT SYSTEM IN $L^2(\mathbb {R}^{2N})$

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  • SANTI RANJAN DAS, RABEETHA VELSAMY, RADHA RAMAKRISHNAN
  • Journal:
    Nagoya Mathematical Journal / Volume 251 / September 2023
    Published online by Cambridge University Press:
    05 June 2023, pp. 734-767
    Print publication:
    September 2023
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  • We consider a general twisted shift-invariant system, $V^{t}(\mathcal {A})$, consisting of twisted translates of countably many generators and study the problem of obtaining a characterization for the system $V^{t}(\mathcal {A})$ to form a frame sequence or a Riesz sequence. We illustrate our theory with some examples. In addition to these results, we study a dual twisted shift-invariant system and also obtain an orthonormal sequence of twisted translates from a given Riesz sequence of twisted translates.

  • Variations on a theorem of Cowling and Price with applications to nilpotent Lie groups

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  • S. Parui, S. Thangavelu
  • Journal:
    Journal of the Australian Mathematical Society / Volume 82 / Issue 1 / February 2007
    Published online by Cambridge University Press:
    09 April 2009, pp. 11-27
    Print publication:
    February 2007
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  • In this paper we prove a new version of the Cowling-Price theorem for Fourier transforms on Rn. Using this we formulate and prove an uncertainty principle for operators. This leads to an analogue of the Cowling-Price theorem for nilpotent Lie groups. We also prove an exact analogue of the Cowling-Price theorem for the Heisenberg group.