What does this research mean for the field?

A smooth orthonormal wavelet and its Fourier transform can be constructed to belong to the extended Gevrey class for σ > 1, providing an example that lies beyond all classical Gevrey classes. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To construct smooth orthonormal wavelets and their Fourier transforms that possess regularity extending beyond classical Gevrey classes.

August 19, 2026Mediterranean Journal of MathematicsOpen Access

Extending Wavelet Regularity Beyond Gevrey Classes

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Authors

FTFilip TomićCroatian Academy of Sciences and Arts STStefan TutićUniversity of Novi Sad MŽMilica ŽigićUniversity of Novi Sad

Discussion

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Implication

Theoretical study demonstrates smooth orthonormal wavelets belonging to extended Gevrey classes, highlighting precise global decay control using expanded low-pass filter supports.

Key Points

To construct smooth orthonormal wavelets and their Fourier transforms that possess regularity extending beyond classical Gevrey classes.
Extended the initial Lemarié–Meyer support of the low-pass filter from [-2π/3, 2π/3] to [-4π/5, 4π/5] using the concept of invariant cycles.
Controlled the decay rate of the low-pass filter near 2π/3 using analytical formulations based on the Lambert W function.
Constructed smooth orthonormal wavelets and Fourier transforms belonging to the extended Gevrey class for σ > 1.
Established global decay estimates for both the wavelet function and its Fourier transform that surpass traditional Gevrey class boundaries.

Cite This Study

Tomić et al. (2026) studied this question.

synapsesocial.com/papers/6a8562eb03308d306e2d5e0c https://doi.org/10.1007/s00009-026-03173-5

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August 19, 2026Mediterranean Journal of MathematicsOpen Access

Extending Wavelet Regularity Beyond Gevrey Classes

View Full Paper

Ask AI

Bookmark

Authors

FTFilip TomićCroatian Academy of Sciences and Arts STStefan TutićUniversity of Novi Sad MŽMilica ŽigićUniversity of Novi Sad

Discussion

Member takes

Implication

Theoretical study demonstrates smooth orthonormal wavelets belonging to extended Gevrey classes, highlighting precise global decay control using expanded low-pass filter supports.

Key Points

To construct smooth orthonormal wavelets and their Fourier transforms that possess regularity extending beyond classical Gevrey classes.
Extended the initial Lemarié–Meyer support of the low-pass filter from [-2π/3, 2π/3] to [-4π/5, 4π/5] using the concept of invariant cycles.
Controlled the decay rate of the low-pass filter near 2π/3 using analytical formulations based on the Lambert W function.
Constructed smooth orthonormal wavelets and Fourier transforms belonging to the extended Gevrey class for σ > 1.
Established global decay estimates for both the wavelet function and its Fourier transform that surpass traditional Gevrey class boundaries.

Cite This Study

Tomić et al. (2026) studied this question.

synapsesocial.com/papers/6a8562eb03308d306e2d5e0c https://doi.org/10.1007/s00009-026-03173-5

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