What does this research mean for the field?

The n-variable Hankel, fractional Hankel, and Bessel wavelet transforms for almost periodic signals can be rigorously constructed using both product-type and windowed spherical approaches, satisfying Parseval-type identities and mapping almost periodic functions into the space of strong limit power functions. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish an n-variable mathematical framework for Hankel, fractional Hankel, and Bessel wavelet transforms acting on almost periodic signals across arbitrary dimensions (n ≥ 2).

September 2, 2026Integral Transforms and Special Functions

Hankel, fractional Hankel, and Bessel wavelet transforms of almost periodic signals: product-type and spherical extensions in n variables

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Authors

BWB. B. Waphare

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Overview

Theoretical analysis establishes multivariable Hankel and Bessel wavelet transforms for almost periodic signals, demonstrating generalized frame decompositions and applications to diffusion equations.

Key Points

To establish an n-variable mathematical framework for Hankel, fractional Hankel, and Bessel wavelet transforms acting on almost periodic signals across arbitrary dimensions (n ≥ 2).
Formulated a coordinate-by-coordinate product-type transform using explicit density arguments and detailed cross-term estimates.
Constructed a windowed spherical transform employing an n-dimensional spherical Bessel kernel to couple spatial variables non-separably.
Tested theoretical properties through numerical boundedness calculations, a non-separable spherical case, and an n-dimensional Bessel-type diffusion equation.
Established Parseval-type identities and proved that almost periodic functions map into the space of strong limit power functions across both constructions.
Derived boundedness estimates and generalized frame decompositions applicable to multi-variable signal domains.
Demonstrated practical utility via closed-form constants in numerical verification, spherical non-separable examples, and exact recovery of prior results for n = 3.

Cite This Study

B. B. Waphare (2026) studied this question.

synapsesocial.com/papers/6a97e305c562ede874ec7953 https://doi.org/10.1080/10652469.2026.2723983

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September 2, 2026Integral Transforms and Special Functions

Hankel, fractional Hankel, and Bessel wavelet transforms of almost periodic signals: product-type and spherical extensions in n variables

View Full Paper

Ask AI

Bookmark

Authors

BWB. B. Waphare

Discussion

Member takes

Overview

Key Points

To establish an n-variable mathematical framework for Hankel, fractional Hankel, and Bessel wavelet transforms acting on almost periodic signals across arbitrary dimensions (n ≥ 2).
Formulated a coordinate-by-coordinate product-type transform using explicit density arguments and detailed cross-term estimates.
Constructed a windowed spherical transform employing an n-dimensional spherical Bessel kernel to couple spatial variables non-separably.
Tested theoretical properties through numerical boundedness calculations, a non-separable spherical case, and an n-dimensional Bessel-type diffusion equation.
Established Parseval-type identities and proved that almost periodic functions map into the space of strong limit power functions across both constructions.
Derived boundedness estimates and generalized frame decompositions applicable to multi-variable signal domains.
Demonstrated practical utility via closed-form constants in numerical verification, spherical non-separable examples, and exact recovery of prior results for n = 3.

Cite This Study

B. B. Waphare (2026) studied this question.

synapsesocial.com/papers/6a97e305c562ede874ec7953 https://doi.org/10.1080/10652469.2026.2723983

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