Nonuniform semi-orthogonal wavelet frames on non-Archimedean local fields of positive characteristic (Q6619553)

This article introduces and characterizes nonuniform semi-orthogonal wavelet frames on non-Archimedean local fields of positive characteristic. The authors generalize traditional wavelet concepts for nonuniform translation structures, extending the utility of wavelets to domains with non-Archimedean fields. Further, by employing Fourier transform techniques, the study establishes tight frame conditions and semi-orthogonality properties that ensure efficient, stable representations. This theoretical framework is supported by equations derived in the frequency domain, providing a robust foundation for constructing nonuniform wavelet systems. The findings have practical implications in signal processing and mathematical analysis, particularly in systems modeled on specialized field structures. The work concludes by highlighting the potential for further applications and developments in this expanding area of research.