Abstract
We investigate spectral multipliers, Bochner–Riesz means and the convergence of eigenfunction expansion corresponding to the Schrödinger operator with anharmonic potential L=−d2dx2+|x|. We show that the Bochner–Riesz profile of the operator L completely coincides with such profile of the harmonic oscillator H=−d2dx2+x2. It is especially surprising because the Bochner–Riesz profile of the one-dimensional standard Laplace operator is known to be essentially different and the case of operators H and L resembles more the profile of multidimensional Laplace operators. Another surprising element of the main obtained result is the fact that the proof is not based on restriction type estimates and instead an entirely new perspective has to be developed to obtain the critical exponent for Bochner–Riesz means convergence.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
