Wavelet Transforms for the Kontorovich-Lebedev-Clifford Transform and Their Applications

Abstract

In this paper, we investigate the continuous wavelet transform within the framework
of the convolution theory of the Kontorovich-Lebedev-Clifford transform, We derive the
reconstruction formula together with the Plancherel and Parseval relations. Additionally,
we introduce localization operators associated with the Kontorovich-Lebedev-Clifford
wavelet transform (KLC-wavelet). Basic properties concerning these operators are proven
to illustrate their boundedness and compactness, and their belonging to the Schatten-von
Neumann class. Furthermore, their corresponding trace formula is determined.