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In this paper we consider \((p,q)\) -frames in shift-invariant spaces of weighted mixed Lebesgue spaces \(L^{p,q}_{\mu }({\mathbb {R}}\times {\mathbb {R}}^d),\) where \(\Phi =\{\phi _1, \cdots , \phi _r\}.\) We prove the equivalence of the frame property and the closedness for the weighted shift-invariant subspace \(V_{\mu }^{p,q}(\Phi ).\)

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Frames in Shift Invariant Spaces of Weighted Mixed Lebesgue Spaces \(L^{p, q}_{\mu }\)

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  • 发表日期：

    2026年

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  • Rocío Balderrama,
  • Carolina Mosquera

摘要

In this paper we consider \((p,q)\) -frames in shift-invariant spaces of weighted mixed Lebesgue spaces \(L^{p,q}_{\mu }({\mathbb {R}}\times {\mathbb {R}}^d),\) where \(\Phi =\{\phi _1, \cdots , \phi _r\}.\) We prove the equivalence of the frame property and the closedness for the weighted shift-invariant subspace \(V_{\mu }^{p,q}(\Phi ).\)