Published on: August 2026
PROPERTIES OF THE KONTOROVICH–LEBEDEV TRANSFORM WITH APPLICATIONS TO MULTI-SCALE SPECTRAL ANALYSIS
VA Sharma
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Abstract
This monograph reconstructs and expands the classical theory of the Kontorovich–Lebedev (KL) transform. Complete statements of the definition, inversion, kernel representations, uniform estimates, asymptotic regimes and the natural domain are given in professional mathematical form with native Office Math Markup Language (OMML) equations. The same analytic apparatus especially the exponential decay of the Macdonald kernel with respect to the spectral variable and the weighted integrability condition that defines the natural domain is then mapped onto contemporary multi-scale problems arising in resilient logistics and supply-chain systems. The mapping draws on the extensive recent literature on the related Fourier–Kontorovich–Lebedev (FKF) transform and its applications to distributional extensions, sequential convergence, spectral analysis of multi-echelon lead times and residue-based resonance extraction, shift-invariant properties, spectral frameworks for resilience, differential properties, as well as digital-twin technology, Industry 5.0 and intelligent logistics, convergent IoT–AI–quantum frameworks, and supply-chain resilience under digital transformation. Supporting figures illustrate the principal estimates, large-order decay, spectral mode decomposition and radial geometries used in continuum models of infrastructure flows.
How to Cite this Paper
Sharma, V. (2026). Properties of the Kontorovich–Lebedev Transform with Applications to Multi-Scale Spectral Analysis. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(8), 1-9. https://doi.org/10.55041/ijcope.v2i8.173
Sharma, VA. "Properties of the Kontorovich–Lebedev Transform with Applications to Multi-Scale Spectral Analysis." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 8, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijcope.v2i8.173.
Sharma, VA. "Properties of the Kontorovich–Lebedev Transform with Applications to Multi-Scale Spectral Analysis." International Journal of Creative and Open Research in Engineering and Management 02, no. 8 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijcope.v2i8.173.
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