Published on: August 2026
DISTRIBUTIONAL EXTENSIONS OF THE KONTOROVICH–LEBEDEV AND FOURIER–KONTOROVICH–LEBEDEV TRANSFORMS
Shinde SM
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Abstract
This paper develops a distributional theory of the KL transform and its two-sided Fourier–Kontorovich–Lebedev (FKF) counterpart. A fundamental distributional inversion identity is established in which a regularized Macdonald kernel converges to the Dirac distribution. The testing-function space underlying the FKF transform is constructed together with its sequential topology, and the transform is defined rigorously by duality. The associated spectral differential operators, time-shift property, and exponential-modulation rule are then derived in the distributional setting. Complex-contour representations and deformation techniques are shown to remain effective for generalized transforms, providing a residue-based framework for identifying multi-scale resonance structures. The resulting distributional spectral language is applied to multi-echelon lead-time analysis, supply-chain dynamics, resilience assessment, and secure digital supply-chain networks. Finally, the framework is positioned within emerging intelligent logistics architectures involving Industry 5.0, digital twins, artificial intelligence, blockchain, and quantum-inspired optimization. The study therefore establishes a unified analytical bridge between generalized KL/FKF spectral theory and modern multi-scale logistics systems, providing a foundation for modelling singular events, extracting spectral signatures, and developing resilience-oriented decision and optimization frameworks.
How to Cite this Paper
SM, S. (2026). Distributional Extensions of the Kontorovich–Lebedev and Fourier–Kontorovich–Lebedev Transforms. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(8), 1-8. https://doi.org/10.55041/ijcope.v2i8.221
SM, Shinde. "Distributional Extensions of the Kontorovich–Lebedev and Fourier–Kontorovich–Lebedev Transforms." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 8, 2026, pp. 1-8. doi:https://doi.org/10.55041/ijcope.v2i8.221.
SM, Shinde. "Distributional Extensions of the Kontorovich–Lebedev and Fourier–Kontorovich–Lebedev Transforms." International Journal of Creative and Open Research in Engineering and Management 02, no. 8 (2026): 1-8. https://doi.org/https://doi.org/10.55041/ijcope.v2i8.221.
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References
- N. Bhosale, M. S. Choudhary, works on double transforms of generalized functions.
- H. Zemanian, Distribution Theory and Transform Analysis, McGraw-Hill.
- Akarshan Gulhane,“ Spectral Analysis for Multi Scale Supply Chain Dynamics and ResidueBased Resonance Extraction in Hybrid-Vehicle Systems,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.141
- Akarshan Gulhane,“ Shift-Invariant Spectral Analysis of Multi-Echelon Supply-Chain Lead Times via the FKF Transform,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.136
- Akarshan Gulhane,“ Spectral Framework Based on the FKF Transform for Supply Chain Dynamics and Resilience,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.140
- Akarshan Gulhane,“ Spectral Differential Properties of the Distributional FKF Transform with Applications to Resilient Supply-Chain Systems,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.139
- Akarshan Gulhane,“ FKL Transform Key Properties, And Applications To Supply-chain Analysis,” International journal of Engineering sciences and Advanced Technology, Published:11-12-2025, Issue: Vol. 25 No. 12 (2025), Page Nos: 596-605, DOI: Https://doi.org/10.64771/ijesat.2025.v25.i12.3816
- Akarshan Gulhane,“ Expanded Treatment Of The Time-Shift Property Of FKF Transform With Supply-Chain Applications,” International journal of Engineering sciences and Advanced Technology, Published:11-12-2025, Issue: Vol. 25 No. 12 (2025), Page Nos: 606 – 616, DOI: Https://doi.org/10.64771/ijesat.2025.v25.i12.3817
- Akarshan Gulhane,“ The FKF Transform: Exponential Modulation Properties And Applications To Secure Digital Supply-Chain Networks,” International journal of Engineering sciences and Advanced Technology, Published:11-12-2025, Issue: Vol. 25 No. 12 (2025), Page Nos: 617 – 623, DOI: Https://doi.org/10.64771/ijesat.2025.v25.i12.3818
- Akarshan Gulhane, “Spectral Differential Properties of the Distributional FKF Transform with Applications to Resilient Supply-Chain Systems,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.139.
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- •Published on: Aug 27 2026
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