Distributional Theory of the Two-Sided Fourier–Kontorovich–Lebedev Transform on Weighted Mixed Testing Spaces

Sharma, V. A.; Shinde, S. M.

doi:https://doi.org/10.55041/ijcope.v2i9.087

Volume 02, Issue 9

Published on: September 2026

DISTRIBUTIONAL THEORY OF THE TWO-SIDED FOURIER–KONTOROVICH–LEBEDEV TRANSFORM ON WEIGHTED MIXED TESTING SPACES

V. A. Sharma S. M. Shinde

Department of Mathematics, Smt. Narsamma Arts, Commerce and Science college, Amravati

DOI:https://doi.org/10.55041/ijcope.v2i9.087

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Abstract

The two-sided Fourier–Kontorovich–Lebedev product kernel is realized as a continuous family of testing functions on the half-strip. A countable multinorm generated by mixed Cartesian and radial operators produces a Fréchet space on which the kernel is a holomorphic section in the frequency variable. Dual pairings therefore define a distributional transform that is holomorphic on an open frequency strip attached to each dual element, jointly continuous on compact spectral sets, and of controlled exponential type in the index. Operational identities for translation, dilation, and mixed Helmholtz generators follow by transferring the operators onto the kernel. A regularized inversion integral recovers every finite-order dual in the weak-star topology, and the construction tensorizes to several Cartesian and radial factors. Growth dictionaries relate the order of a dual to the admissible width of the frequency strip and to the polynomial degree in the Kontorovich–Lebedev index. The resulting calculus supplies a spectral representation for mixed partial operators on the half-strip and a uniqueness theorem on connected spectral regions.

Keywords: distributional Fourier–Kontorovich–Lebedev transform, weighted testing space, Macdonald kernel, strip holomorphy, weak-star inversion, mixed Helmholtz multiplier

How to Cite this Paper

Sharma, V. A. & Shinde, S. M. (2026). Distributional Theory of the Two-Sided Fourier–Kontorovich–Lebedev Transform on Weighted Mixed Testing Spaces. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(9), 1-9. https://doi.org/10.55041/ijcope.v2i9.087

Sharma, V., and S. Shinde. "Distributional Theory of the Two-Sided Fourier–Kontorovich–Lebedev Transform on Weighted Mixed Testing Spaces." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 9, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijcope.v2i9.087.

Sharma, V., and S. Shinde. "Distributional Theory of the Two-Sided Fourier–Kontorovich–Lebedev Transform on Weighted Mixed Testing Spaces." International Journal of Creative and Open Research in Engineering and Management 02, no. 9 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijcope.v2i9.087.

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References

D. Sharma, “Analyticity of Distribution Generalized Fourier-Stieltjes Transforms,” 2012. The paper extends the Fourier–Stieltjes transform to a distributional generalized setting and establishes an analyticity theorem.

D. Sharma, “Operators on the Distributional Generalized Two-Dimensional Fractional Fourier Transform,” International Journal of Modern Mathematical Sciences, vol. 9, no. 1, pp. 39–45, 2014.

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D. Sharma and P. B. Deshmukh, “Generalized Two-Dimensional Fractional Mellin Transform,” Proc. IEEE, pp. 900–903.

D. Sharma and P. B. Deshmukh, “S-Type Spaces for Two Dimensional Fractional Fourier-Mellin Transform,” International Journal of Advances in Science, Engineering and Technology, pp. 74–76, June 2015.

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D. Sharma, “Operational Calculus for Two Dimensional Fractional Fourier-Mellin Transform,” International Journal of Multidisciplinary Research and Development, vol. 3, no. 1, pp. 99–104, 2016.

D. Sharma and P. B. Deshmukh, “Analyticity of Two-Dimensional Fractional Fourier-Mellin Transform,” International Journal of Engineering Sciences & Research Technology, 2016, DOI 10.5281/zenodo.47633.

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