@article{d16af15bd4234beabf71d806231bf9b0,
title = "On a problem by Hans Feichtinger",
abstract = "In this paper, we solve a spectral problem about positive semi-definite trace-class pseudodifferential operators on modulation spaces which was posed by H. Feichtinger. Later, C. Heil and D. Larson rephrased the problem in the broader setting of positive semi-definite trace-class operators on a separable Hilbert space. Our solution consists in constructing a counterexample that solves Hans Feichtinger{\textquoteright}s problem by first solving this second problem.",
keywords = "Modulation spaces, Pseudodifferential operators, Time-frequency analysis, Trace-class operators, Wilson bases",
author = "Radu Balan and Okoudjou, {Kasso A.} and Anirudha Poria",
note = "Funding Information: R. Balan and K. A. Okoudjouwere partially supported by ARO grantW911NF1610008. R. Balan was also partially supported by the NSF grant DMS- 1413249 and the LTS grant H9823013D00560049. K. A. Okoudjou was also partially supported by a grant from the Simons Foundation #319197. This material is partially based upon work supported by the National Science Foundation under Grant No. DMS- 1440140while K. A. Okoudjouwas in residence at theMathematical Sciences Research Institute in Berkeley, California, during the Spring 2017 semester. A. Poria is grateful to the United States-India Educational Foundation for providing the Fulbright-Nehru Doctoral Research Fellowship, and to the Department of Mathematics, University of Maryland, College Park, USA for the support provided during the period of this work. He would also like to express his gratitude to the NorbertWiener Center for Harmonic Analysis and Applications at the University of Maryland, College Park for its kind hospitality, and the Indian Institute of Technology Guwahati, India for its support. Publisher Copyright: {\textcopyright} 2018, Element D.O.O. All rights reserved.",
year = "2018",
month = sep,
doi = "10.7153/oam-2018-12-53",
language = "English",
volume = "12",
pages = "881--891",
journal = "Operators and Matrices",
issn = "1846-3886",
number = "3",
}