Frames and the Feichtinger conjecture
By Peter G. Casazza, Ole W. Christensen, A. Lindner, Roman Vershynin. 2004
102 citations recorded by the source corpus.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8edaca0d4776a4f3f54881ebfb1b0c5ed5c2e037
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
- Christopher Heil
- Gitta Kutyniok
- Y. Belov
- Peter G. Casazza
- A. Borichev
- Karlheinz Gröchenig
- Radu V. Balan
- Adam W. Marcus
In Mathematical Physics
- Christopher Heil
- Y. Belov
- A. Borichev
- Adam W. Marcus
- T. Mengestie
- Daniel A. Spielman
- Kristian Seip
- Gitta Kutyniok
Citations in the corpus
- Interlacing families II: Mixed characteristic polynomials and the Kadison{Singer problem (2013, background): “njectures [And79a, And79b, And81], Weaver’s discrepancy theoretic KSr and KS′ r conjectures [Wea04], the Bourgain-Tzafriri Conjecture[BT91, CT06], and the Feichtinger Conjecture and the Rǫ-Conjecture [CCLV05]. Many approaches to these problems have been proposed; and, under slightly stronger hypothe”
- Discrete Hilbert transforms on sparse sequences (2009, background): “In an intriguing series of papers [11, 12, 14, 15], it has been revealed that the Feichtinger conjecture is equivalent to the long-standing Kadison–Singer conjecture [22].”
- Linear Independence of Finite Gabor Systems (2006, result): “This conjecture is open and has recently been shown to be equivalent to the deep and longstanding Kadison–Singer Conjecture in operator theory, which has been open since 1959 [85]; see [26], [ 23 ] for the proof of the equivalence.”
- Density, overcompleteness, and localization of frames (2006, result): “It is shown in [ CCLV03 ], [CV03], [CT05] that Feichtinger’s conjecture equivalent to the celebrated Kadison{Singer (paving) conjecture, and that both of these are equivalent to a conjectured generalization of the Bourgain{Tzafriri restricted invertibility theorem.”
- Frames of subspaces (2003, background): “Justrecently Casazza, Christensen, Lindner, and Vershynin [5] proved that the so-called "Feichtingerconjecture" isequivalentto the weak Bourgain-Tzafririconjecture.”
- Sampling and interpolation in large Bergman and Fock spaces (2007, background): “The famous Feichtinger conjecture (see, for example, [9,10]) claims that any frame in a Hilbert space is a finite union of Riesz basic sequences.”