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A Structural Analysis of FMRA in L2(R)n

Author(s):Bijumon Ramalayathil¹, Haseena C², Priyanka P³, Jimly Manuel⁴

Affiliation: ¹²³⁴ Department of Mathematics ,¹²³⁴ Mahatma Gandhi College, Iritty, Keezhur P.O., Kerala, India.

Page No: 10-13

Volume issue & Publishing Year: Volume 2 Issue 10,Oct-2025

Journal: International Journal of Advanced Multidisciplinary Application.(IJAMA)

ISSN NO: 3048-9350

DOI: https://doi.org/10.5281/zenodo.17338877

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Abstract:
Frame Multiresolution Analysis (FMRA) extends the classical concept of multiresolution analysis to the context of frames in Hilbert spaces. In this paper, we investigate FMRA in the superspace L2(R)n and establish that the frame property of the system {Tkϕ1 ⊕ · · · ⊕ ϕn : k ∈ Z} in V0 is preserved under dilations by the operator UC. Specifically, we prove that the dilated-translated system {Uj Tkϕ1 ⊕ · · · ⊕ ϕn : k ∈ Z} forms a frame for Vj with the same frame bounds as in V0. This result demonstrates the stability of FMRA frames under generalized dilation and translation operators in L2(R)n, facilitating their application to multiple signal processing and superwavelet constructions

Keywords: Frame Multiresolution Analysis (FMRA), superspace frames, dilation and translation invariance.AMS Subject Classification: 42C40, 42C15.

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