Ergodic Schrödinger operators in the infinite measure setting

Ergodic Theory of Markov Chains Admitting an Infinite Invariant Measure.

Ergodic and Spectral Analysis of Certain Infinite Measure Preserving Transformations

0. Introduction. Throughout this paper T will denote a measure preserving transformation on a cr-finite infinite measure space (X, (B, m) which is point isomorphic with the Lebesgue measure space of the real line. Unless otherwise stated, T will be one-one. Equations involving functions or sets will always be interpreted modulo sets of measure zero. T is said to be ergodic if T~1E = E, ££(B, im...

Convergence of Schrödinger Operators

For a large class, containing the Kato class, of real-valued Radon measures m on R the operators −∆ + ε∆ + m in L(R, dx) tend to the operator −∆ +m in the norm resolvent sense, as ε tends to zero. If d ≤ 3 and a sequence (μn) of finite real-valued Radon measures on R converges to the finite real-valued Radon measure m weakly and, in addition, supn∈N μ ± n (R) < ∞, then the operators −∆ + ε∆ + μ...

Schrödinger operators in the twentieth century *

This paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics.

Schrödinger Operators with Singular Potentials †

We describe classical and recent results on the spectral theory of Schrödinger and Pauli operators with singular electric and magnetic potentials