Identifies Parseval frames from monomials in L2(T,μ) for singular μ with frames from model subspaces H(φ) and characterizes measures reproducing kernels contained in such subspaces.
Fourier bases and Fourier frames on self-affine measures
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abstract
This paper gives a review of the recent progress in the study of Fourier bases and Fourier frames on self-affine measures. In particular, we emphasize the new matrix analysis approach for checking the completeness of a mutually orthogonal set. This method helps us settle down a long-standing conjecture that Hadamard triples generates self-affine spectral measures. It also gives us non-trivial examples of fractal measures with Fourier frames. Furthermore, a new avenue is open to investigate whether the Middle Third Cantor measure admits Fourier frames.
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math.CA 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures
Identifies Parseval frames from monomials in L2(T,μ) for singular μ with frames from model subspaces H(φ) and characterizes measures reproducing kernels contained in such subspaces.