We introduce the localization operator associated with the linear canonical continuous Dunkl wavelet transform. We analyze the boundedness of the operator for various classes of symbols and wavelet functions. We also establish the compactness of the localization operator on spaces, where . Additionally, we explore the properties of the localization operator in Schatten-von Neumann classes and demonstrate that, with appropriate choices of symbols and wavelet functions, the localization operator can be identified as both a trace class operator and a Hilbert–Schmidt operator.

We develop a novel mobility-aware transformer-driven tiered structure (MASSFormer) based co-operative spectrum sensing method that effectively models the spatio-temporal dynamics of user movements. Unlike existing methods, our method considers a dynamic scenario involving mobile primary users (PUs) and secondary users (SUs) and addresses the complexities introduced by user mobility. The transformer architecture utilizes an attention mechanism, allowing the proposed method to model the temporal dynamics of user mobility by effectively capturing long-range dependencies. The proposed method first computes tokens from the sequence of covariance matrices (CMs) for each SU. It processes them in parallel using the SU-transformer to learn the spatio-temporal features at SU-level. Subsequently, the collaborative transformer learns the group-level PU state from all SU-level feature representations. The main goal of predicting the PU states at each SU-level and group-level is to improve detection performance even more. The proposed method is tested under imperfect reporting channel scenarios to show robustness. The efficacy of our method is validated with simulation results that demonstrate its higher performance compared to existing methods in terms of detection probability Pd, sensing error, and classification accuracy (CA).

We define the composition of wavelet transforms and obtain its Parsevals's identity. Furthermore, we discuss the convolution operator and continuous Dunkl wavelet transform as time-invariant filters. The physical interpretation and potential application of time-invariant filter involving Fredholm type integral are obtained. © 2024 Informa UK Limited, trading as Taylor & Francis Group.

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The dual convolution structure for the Mehler-Fock transform is defined and obtained its estimates on Lebesgue space. Next, the two symbols ?(x, ?) and ?(y, ?) as an inverse Mehler-Fock transform of some measurable functions are introduced and defined the two pseudo-differential operators P and Q respectively. Moreover, the product of two pseudo-differential operators is shown as a pseudo-differential operator. Furthermore, the boundedness of this operator in Sobolev-type space by using the dual convolution is shown and discussed the some special cases.

The main objective of this paper is to study the composition of continuous Kontorovich-Lebedev wavelet transform (KL-wavelet transform) and wave packet transform (WPT) based on the Kontorovich-Lebedev transform (KL-transform). Estimates for KL-wavelet and KL-wavelet transform are obtained, and Plancherel’s relation for composition of KL-wavelet transform and WPT-transform are derived. Recon-struction formula for WPT associated to KL-transform is also deduced and at the end Calderon’s formula related to KL-transform using its convolution property is obtained.