Abstract :

This Paper Develops A Distributional Theory For The Two-sided Fourier–Kontorovich–Lebedev (FKF) Transform And Demonstrates Its Relevance To The Analysis Of Modern Supply-chain Systems. The FKF Transform Combines The Classical Fourier Transform In A Temporal Variable With The Kontorovich–Lebedev Transform (built Upon The Macdonald Function Of Purely Imaginary Order) In A Positive Scale Or Intensity Variable. After Recalling The Underlying Testing-function Space And The Extension Of The Transform To Generalized Functions, We Establish The Principal Operational Properties, With Particular Emphasis On The Time-shift Property. A Time Delay Appears Solely As A Multiplicative Phase Factor In The Fourier Spectral Variable, Leaving The Magnitude Spectrum Invariant. This Phase-only Signature Is Shown To Be Especially Useful For The Detection And Characterization Of Lead-time Delays, Transportation Lags, And Disruption Propagation In Supply Chains. We Then Outline A Conceptual FKF-based Workflow That Maps Multi-dimensional Supplychain Signals (demand, Inventory, Distance, Intensity) Into A Joint Frequency–scale Domain, Enabling Spectral Filtering, Anomaly Detection, And Resilience Assessment. Assumptions, Computational Limitations, And Directions For Future Research Are Discussed. The Framework Bridges Classical Distributional Transform Theory With Contemporary Digitaltwin And Resilience-oriented Supply-chain Analytics. Keywords: FKF Transform; Macdonald Function; Distributional Transforms; Time-shift Property; Phase Spectrum; Supply-chain Resilience; Lead-time Analysis; Spectral Methods; Digital Twins

Published:

11-12-2025

Issue:

Vol. 25 No. 12 (2025)

Page Nos:

606 - 616

Section:

Articles

License:

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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