Imbedded singular continuous spectrum for Schrödinger operators
نویسندگان
چکیده
منابع مشابه
Imbedded Singular Continuous Spectrum for Schrödinger Operators
We construct examples of potentials V (x) satisfying |V (x)| ≤ h(x) 1+x , where the function h(x) is growing arbitrarily slowly, such that the corresponding Schrödinger operator has imbedded singular continuous spectrum. This solves one of the fifteen “twenty-first century” problems for Schrödinger operators posed by Barry Simon in [22]. The construction also provides the first example of a Sch...
متن کاملOperators with Singular Continuous Spectrum
The Baire category theorem implies that the family, F,of dense sets G6 in a fixed metric space, X , is a candidate for generic sets since it is closed under countable intersections; and if X is perfect (has no isolated point), then A E F has uncountable intersections with any open ball in X. There is a long tradition of soft arguments to prove that certain surprising sets are generic. For examp...
متن کاملSingular Continuous Spectrum for Palindromic Schrödinger Operators
We give new examples of discrete Schrödinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potential x in X for which the operator has no eigenvalues implies that there is a generic set in X for which the operator has purely singular continuous spectrum. A su...
متن کاملSingular Continuous Spectrum for Palindromic Schrδdinger Operators
We give new examples of discrete Schrδdinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potential x in X for which the operator has no eigenvalues implies that there is a generic set in X for which the operator has purely singular continuous spectrum. A su...
متن کاملSchrödinger 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
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2005
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-05-00489-3