What question did this study set out to answer?

The aim is to demonstrate the existence and properties of smooth band-limited multiresolution analysis and orthonormal Meyer wavelets for expansive dilations.

August 7, 2026Revista Matemática IberoamericanaOpen Access

Meyer wavelets for rational dilations

View Full Paper

Ask AI

Bookmark

The aim is to demonstrate the existence and properties of smooth band-limited multiresolution analysis and orthonormal Meyer wavelets for expansive dilations.
Proved existence of smooth band-limited MRA for any expansive dilation in any spatial dimension.
Showed orthonormal Meyer wavelets' existence for rational entries and expansive dilations across multiple dimensions.
Established conditions for localization of orthogonal MRA wavelets and their dependence on rational entries.
Confirmed that smooth, compactly supported Fourier transform wavelets exist for rational expansive dilations.
Demonstrated that localized MRA wavelets can only exist for rational entries in expansive dilations, establishing optimality.
Extended one-dimensional results of previous studies to a multi-dimensional setting.

Discussion

No takes yet. Share an insight, caveat, or question.

Implication

Randomized trial demonstrates the existence of wavelets for expansive dilations with rational entries, indicating optimality in multi-dimensional spaces.

Cite This Study

Marcin Bownik (2026) studied this question.

synapsesocial.com/papers/6a758b54847ab6d26c01eb0a https://doi.org/10.4171/rmi/1649

View Full Paper

Ask AI

Bookmark

Implication

Randomized trial demonstrates the existence of wavelets for expansive dilations with rational entries, indicating optimality in multi-dimensional spaces.

Meyer wavelets for rational dilations

Key Points

Discussion

Implication

Cite This Study

Meyer wavelets for rational dilations

Key Points

Discussion

Implication

Cite This Study

Also Consider

Also Consider