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The nonexistence
of cubic Legendre multiplier sequences
Tamás Forgács, James Haley, Rebecca Menke and Carlee Simon
Vol. 7 (2014), No. 6, 773–786
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Abstract |
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Our main result is the proof of the recently conjectured nonexistence of cubic Legendre multiplier sequences. We also give an alternative proof of the nonexistence of linear Legendre multiplier sequences using a method that will allow for a more methodical treatment of sequences interpolated by higher degree polynomials. |
Keywords
Legendre multiplier sequences, reality preserving linear
operators, symbol of a linear operator, coefficients of
Legendre-diagonal differential operators
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Mathematical Subject Classification 2010
Primary: 26C10, 30C15
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Milestones
Received: 16 October 2013
Revised: 9 January 2014
Accepted: 24 January 2014
Published: 20 October 2014
Communicated by Michael Dorff
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Authors |
| Tamás Forgács | |
| Department of Mathematics California State University Fresno 5245 North Backer Ave, M/S PB 108 Fresno, CA 93740-8001 United States |
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| James Haley | |
| Mathematics University of Rochester 915 Hylan Building RC Box 270138 Rochester, NY 14627 United States |
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| Rebecca Menke | |
| Department of Mathematics and
Statistics Auburn University 221 Parker Hall Auburn, AL 36849 United States |
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| Carlee Simon | |
| Department of Mathematics Davidson College Box 7129 Davidson, NC 28035 United States |
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