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arXiv · 2608.18879

Adaptive resolution frames: A multilevel framework in Hilbert spaces

Jahangir Cheshmavar
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Abstract

We introduce adaptive resolution frames (AR-frames), a class of weighted frames equipped with a partitioned index structure that models multiple resolution levels in Hilbert spaces. We establish a block-triangular representation of the associated operators and prove the convergence of an iterative reconstruction method with explicit error estimates. We further derive optimal block-diagonal preconditioners that minimize the iteration error and obtain stability results showing that AR-frames and their canonical reconstruction operators remain stable under sufficiently small weighted perturbations. These results provide a unified framework for efficient reconstruction and perturbation analysis of AR-frames.

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Jahangir Cheshmavar. 2026-08-19. Adaptive resolution frames: A multilevel framework in Hilbert spaces. https://arxiv.org/abs/2608.18879

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