Subspace Weyl-Heisenberg frames
- Cite this article as:
- Gabardo, JP. & Han, D. The Journal of Fourier Analysis and Applications (2001) 7: 419. doi:10.1007/BF02514505
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A Weyl-Heisenberg frame (WH frame) for L2(ℝ) allows every square integrable function on the line to be decomposed into the infinite sum of linear combination of translated and modulated versions of a fixed function. Some sufficient conditions for g ∈ L2(ℝ) to be a subspace Weyl-Heisenberg frame were given in a recent work  by Casazza and Christensen. Obviously every invariant subspace (under translation and modulation) is cyclic if it has a subspace WH frame. In the present article we prove that the cyclicity property is also sufficient for a subspace to admit a WH frame. We also investigate the dilation property for subspace Weyl-Heisenberg frames and show that every normalized tight subspace WH frame can be dilated to a normalized tight WH frame which is “maximal” In other words, every subspace WH frame is the compression of a WH frame which cannot be dilated anymore within the L2(ℝ) space.