Distributional Extension of the FKF Transform and Its Relevance to Supply-Chain Systems
- 1PTC Software Inc
Abstract
This paper develops the distributional theory of the FKF transform and demonstrates its relevance to the analysis of modern supply-chain systems. The FKF transform combines a Fourier factor that captures temporal oscillations, frequencies and lead-time cycles with a Kontorovich–Lebedev (KL) factor built from the Macdonald function of imaginary order. The latter is naturally adapted to positive scale, distance or intensity variables that arise throughout logistics networks. After reviewing the classical definition on suitable testing-function spaces, the transform is extended to a broad class of generalized functions in the sense of Zemanian. The distributional extension permits idealized impulses, abrupt demand shocks, capacity collapses and other singular forcing terms to be treated within a single rigorous spectral framework. Applications to supply-chain resilience, disruption modelling, multi-scale inventory intensity and digital-twin spectral diagnostics are discussed. Numerical approximation formulae for discrete operational data are also provided, together with recommendations for future research and computational practice.
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BibTeX
@article{gulhane2026distributional,
title = {{Distributional Extension of the FKF Transform and Its Relevance to 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.v2i8.137},
url = {https://doi.org/10.55041/ijcope.v2i8.137},
note = {CC BY-NC},
}
RIS
TY - JOUR
TI - Distributional Extension of the FKF Transform and Its Relevance to 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.v2i8.137
UR - https://doi.org/10.55041/ijcope.v2i8.137
AB - This paper develops the distributional theory of the FKF transform and demonstrates its relevance to the analysis of modern supply-chain systems. The FKF transform combines a Fourier factor that captures temporal oscillations, frequencies and lead-time cycles with a Kontorovich–Lebedev (KL) factor built from the Macdonald function of imaginary order. The latter is naturally adapted to positive scale, distance or intensity variables that arise throughout logistics networks. After reviewing the classical definition on suitable testing-function spaces, the transform is extended to a broad class of generalized functions in the sense of Zemanian. The distributional extension permits idealized impulses, abrupt demand shocks, capacity collapses and other singular forcing terms to be treated within a single rigorous spectral framework. Applications to supply-chain resilience, disruption modelling, multi-scale inventory intensity and digital-twin spectral diagnostics are discussed. Numerical approximation formulae for discrete operational data are also provided, together with recommendations for future research and computational practice.
SN - 3108-1754
ER -