The Spectral Function of Shift-Invariant Spaces

By Marcin Bownik, Ziemowit Rzeszotnik. 2003

50 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Geophysics

View Paper: https://www.semanticscholar.org/paper/b3670516f9ba72d01703b04877fbc58986ac8965

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Christopher Heil
2. Karlheinz Gröchenig

In Computer Vision and Pattern Recognition

1. Christopher Heil
2. Karlheinz Gröchenig
3. Götz E. Pfander

In Geophysics

1. Christopher Heil
2. Karlheinz Gröchenig

Citations in the corpus

• Invariance of a Shift-Invariant Space (2008, unknown): “For properties of the dimension function of a SIS, see for example [2] or [5].”
• Linear Independence of Finite Gabor Systems (2006, background): “on von Neumann algebras is given in [44], and a new proof appears in [ 20 ].”
• History and Evolution of the Density Theorem for Gabor Frames (2007, background): “Bownik and Rzeszotnik gave a proof of part (c) in [27] based on the use of the spectral function rather than the machinery of von Neumann algebras.”
• The Structure of Translation-Invariant Spaces on Locally Compact Abelian Groups (2015, unknown): “The results of Rzeszotnik and the first author [7,8] show that the spectral function on Rn scales nicely when an SI space is dilated by an invertible matrix.”