Vol. 7, No. 6, 2014

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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

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.

Legendre multiplier sequences, reality preserving linear operators, symbol of a linear operator, coefficients of Legendre-diagonal differential operators
Mathematical Subject Classification 2010
Primary: 26C10, 30C15
Received: 16 October 2013
Revised: 9 January 2014
Accepted: 24 January 2014
Published: 20 October 2014

Communicated by Michael Dorff
Tamás Forgács
Department of Mathematics
California State University Fresno
5245 North Backer Ave, M/S
PB 108
Fresno, CA 93740-8001
United States
James Haley
University of Rochester
915 Hylan Building
RC Box 270138
Rochester, NY 14627
United States
Rebecca Menke
Department of Mathematics and Statistics
Auburn University
221 Parker Hall
Auburn, AL 36849
United States
Carlee Simon
Department of Mathematics
Davidson College
Box 7129
Davidson, NC 28035
United States