2021/11/23 by Marianna Chatzakou, Julio Delgado, Chatzakou, Marianna +3
Mathematics · #Spectral Theory in Mathematical Physics #Advanced Mathematical Physics Problems #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2111.11917
In this work we study a class of anharmonic oscillators on ℝn corresponding to Hamiltonians of the form A(D)+V(x), where A(ξ) and V(x) are C∞ functions enjoying some regularity conditions. Our class includes fractional relativistic Schrödinger operators and anharmonic oscillators with fractional potentials. By associating a Hörmander metric we obtain spectral properties in terms of Schatten-von Neumann classes for their negative powers and derive from them estimates on the rate of growth for the eigenvalues of the operators A(D)+V(x). This extends the analysis in the first part of our work, where the case of polynomial A and V has been analysed.