Pure point diffraction and cut and project schemes for measures: the smooth case

Lenz D, Richard C (2007)


Publication Type: Journal article

Publication year: 2007

Journal

Publisher: Springer Verlag (Germany)

Book Volume: 256

Pages Range: 347-378

Journal Issue: 2

URI: http://link.springer.com/article/10.1007/s00209-006-0077-0

DOI: 10.1007/s00209-006-0077-0

Abstract

We present a cut and project formalism based on measures and continuous weight functions of sufficiently fast decay. The emerging measures are strongly almost periodic. The corresponding dynamical systems are compact groups and homomorphic images of the underlying torus. In particular, they are strictly ergodic with pure point spectrum and continuous eigenfunctions. Their diffraction can be calculated explicitly. Our results cover and extend corresponding earlier results on dense Dirac combs and continuous weight functions with compact support. They also mark a clear difference in terms of factor maps between the case of continuous and non-continuous weight functions.

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APA:

Lenz, D., & Richard, C. (2007). Pure point diffraction and cut and project schemes for measures: the smooth case. Mathematische Zeitschrift, 256(2), 347-378. https://dx.doi.org/10.1007/s00209-006-0077-0

MLA:

Lenz, Daniel, and Christoph Richard. "Pure point diffraction and cut and project schemes for measures: the smooth case." Mathematische Zeitschrift 256.2 (2007): 347-378.

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