Gabor Frame Multiplier Analysis

The theory of frames for a Hilbert space plays an important role in the areas such as signal processing, image processing, data compression, sampling theory. As an important kind of frame, Gabor frames possess great values for research in the fields such as optics, signal detection, noise removal, quantum theory. A Gabor frame multiplier is a bounded linear operator that preserves the original Parseval Gabor frame window function. It has great theoretical significance as it helps to analyze the inner structure of Gabor frames. In this paper, we mainly study the sufficient and necessary conditions for a Gabor frame multiplier which has the form A_σ : g(t) → g(σ~-1{t))(σ : R→ R is a bijective measure-preserving mapping).