We study for , the family of self-adjoint operators
in and show that if is even then gives the unique minimum of the lowest eigenvalue of this family of operators. Combined with earlier results this gives that for any , the lowest eigenvalue has a unique minimum as a function of .
Cite this article
Søren Fournais, Mikael Persson Sundqvist, A uniqueness theorem for higher order anharmonic oscillators. J. Spectr. Theory 5 (2015), no. 2, pp. 235–249DOI 10.4171/JST/96