Compactly supported bounded frames on Lie groups
Vignon Oussa

TL;DR
This paper constructs compactly supported, smooth frames on certain Lie groups using induced representations, extending previous work and enabling well-localized frames relevant to time-frequency analysis and wavelet theories.
Contribution
It proves the existence of compactly supported, smooth frames for induced representations on Lie groups, extending prior results to more general groups and solving an open problem.
Findings
Existence of countable sets and functions forming frames on Lie groups
Construction of continuous and smooth functions for frames
Extension of previous work to general connected Lie groups
Abstract
Let be a Lie group where are closed connected subgroups of and is an exponential solvable Lie group which is normal in Suppose furthermore that admits a unitary character corresponding to a linear functional of its Lie algebra. We assume that the map defines an immersion at the identity of . Fixing a Haar measure on we consider the unitary representation of obtained by inducing This representation which is realized as acting in is generally not irreducible, and we do not assume that it satisfies any integrability condition. One of our main results establishes the existence of a countable set and a function which is compactly supported and bounded…
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Advanced Harmonic Analysis Research · Advanced Mathematical Physics Problems
