Delone sets and Riesz basis
Copyright policy )Delone sets and Riesz basis
A standard technique of obtaining a Riesz basis for a Hilbert space is by considering exponential maps over a periodic set. The author obtains analogues of the well-known Kadec's 1/4-theorem by replacing the periodic set with a sufficiently close Delone set and constructs Riesz bases for the Hilbert spaces \(L^2 (W_A(0))\) and \(H^1 [-\pi,\pi]\) (where \(W_A(0)\) is a suitable transformation of the Voronoi cell at \(0\in Z^N)\) by considering exponential maps over this Delone set.
- Kyushu University Japan
42B05, Delone set, Voronoi cell, exponential maps, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Hilbert space, 46C05, Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.), periodic set, Riesz basis
42B05, Delone set, Voronoi cell, exponential maps, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Hilbert space, 46C05, Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.), periodic set, Riesz basis
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