@article{11b815362f3142b7b26b646182e51b8c,
title = "Improved bounds in Weaver and Feichtinger conjectures",
abstract = " We sharpen the constant in the KS 2 Conjecture of Weaver [31] that was given by Marcus, Spielman and Srivastava [28] in their solution of the Kadison-Singer problem. We then apply this result to prove optimal asymptotic bounds on the size of partitions in the Feichtinger Conjecture.",
author = "Marcin Bownik and Pete Casazza and Marcus, {Adam W.} and Darrin Speegle",
note = "Funding Information: The first author was partially supported by NSF grant DMS-1265711. The second author was supported by NSF grant DMS-1609760, NSF grant ATD-1321779, and ARO grant W911NF-16-1-0008. The fourth author was partially supported by a grant from the Simons Foundation #244953. The work on this paper was initiated during the AIM workshop {"}Beyond Kadison-Singer: paving and consequences{"} on December 1-5, 2014. Funding Information: The first author was partially supported by NSF grant DMS-1265711. The second author was supported by NSF grant DMS-1609760, NSF grant ATD-1321779, and ARO grant W911NF-16-1-0008. The fourth author was partially supported by a grant from the Simons Foundation #244953. The work on this paper was initiated during the AIM workshop “Beyond Kadison–Singer: paving and consequences” on December 1–5, 2014. Publisher Copyright: {\textcopyright} 2019 Walter de Gruyter GmbH, Berlin/Boston.",
year = "2019",
doi = "10.1515/crelle-2016-0032",
language = "English (US)",
volume = "2019",
pages = "267--293",
journal = "Journal fur die Reine und Angewandte Mathematik",
issn = "0075-4102",
publisher = "Walter de Gruyter GmbH & Co. KG",
number = "749",
}