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Some anisotropic Schrödinger operators without singular spectrum. (English) Zbl 0851.35098

A typical example of an anisotropic potential considered in the paper is given by the formula \[ V(x)= V_1(x_1/ |x_1|) V_2(x_2),\quad x= (x_1, x_2). \] Thus it is a homogeneous function of order zero in the variable \(x_1\). The absence of the singular spectrum and some resolvent estimates are established.

MSC:

35P05 General topics in linear spectral theory for PDEs
47A10 Spectrum, resolvent
35J10 Schrödinger operator, Schrödinger equation
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