Spectral Differential Properties of the Distributional FKF Transform with Applications to Resilient Supply-Chain Systems
- 1PTC Software Inc
Abstract
This paper develops the distributional theory of the two-sided Fourier–Kontorovich–Lebedev (FKF) transform, a hybrid integral transform that combines the Fourier kernel in the temporal variable with the Macdonald (modified Bessel) kernel of imaginary order in a positive scale variable. The transform is extended to a broad class of generalized functions via a carefully constructed test-function space of Gelfand–Shilov type. Central attention is given to the spectral differential property associated with the modified-Bessel operator, which converts differential action in the positive variable into multiplication by −q² in the spectral domain. The property is expanded with higher-order operators, mixed Fourier–KL rules, and solution formulae for model linear PDEs. Applications of the FKF spectral differential property to supply-chain systems are developed in detail: multi-scale inventory dynamics, disruption-intensity resilience analysis, digital-twin spectral monitoring, and discrete numerical implementation for operational data. The framework is positioned within recent advances in intelligent logistics, digital twins, quantum-inspired optimization, and supply-chain resilience. Concrete recommendations for research and practice, together with a recommended computational form for discrete and noisy data, conclude the work.
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BibTeX
@article{gulhane2026spectral,
title = {{Spectral Differential Properties of the Distributional FKF Transform with Applications to Resilient Supply-Chain Systems}},
author = {Akarshan Gulhane},
journal = {International Journal of Creative and Open Research in Engineering and Management},
year = {2026},
month = aug,
doi = {10.55041/ijcope.v2i8.139},
url = {https://doi.org/10.55041/ijcope.v2i8.139},
note = {CC BY-NC},
}
RIS
TY - JOUR
TI - Spectral Differential Properties of the Distributional FKF Transform with Applications to Resilient Supply-Chain Systems
AU - Akarshan Gulhane
PY - 2026
DA - 2026/08/17
JO - International Journal of Creative and Open Research in Engineering and Management
DO - 10.55041/ijcope.v2i8.139
UR - https://doi.org/10.55041/ijcope.v2i8.139
AB - This paper develops the distributional theory of the two-sided Fourier–Kontorovich–Lebedev (FKF) transform, a hybrid integral transform that combines the Fourier kernel in the temporal variable with the Macdonald (modified Bessel) kernel of imaginary order in a positive scale variable. The transform is extended to a broad class of generalized functions via a carefully constructed test-function space of Gelfand–Shilov type. Central attention is given to the spectral differential property associated with the modified-Bessel operator, which converts differential action in the positive variable into multiplication by −q² in the spectral domain. The property is expanded with higher-order operators, mixed Fourier–KL rules, and solution formulae for model linear PDEs. Applications of the FKF spectral differential property to supply-chain systems are developed in detail: multi-scale inventory dynamics, disruption-intensity resilience analysis, digital-twin spectral monitoring, and discrete numerical implementation for operational data. The framework is positioned within recent advances in intelligent logistics, digital twins, quantum-inspired optimization, and supply-chain resilience. Concrete recommendations for research and practice, together with a recommended computational form for discrete and noisy data, conclude the work.
SN - 3108-1754
ER -