Book Review: Schrödinger-type operators with continuous spectra
نویسندگان
چکیده
منابع مشابه
Asymptotics and Gaps in the Spectra of Magnetic Schrödinger Operators
In this paper, we study an L version of the semiclassical approximation of magnetic Schrödinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence of an arbitrary large number of gaps in the spectrum of these operators, in the semiclassical limit as the coupling constant μ goes to zero.
متن کاملSome Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials
where the potential V belongs to Bq1 for q1 ≥ n/2. We are interested in the L boundedness of the operator∇4H−1, where the potential V satisfies weaker condition than that in 5, Theorem 1, 2 . The estimates of some other operators related to Schrödinger-type operators can be found in 2, 5 . Note that a nonnegative locally L integrable function V on R is said to belong to Bq 1 < q < ∞ if there ex...
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 کاملWiener - Hopf Operators and Absolutely Continuous Spectra
CONTINUOUS SPECTRA. II BY C. R. PUTNAM Communicated by Maurice Heins, November 1, 1967 1. This paper is a continuation of [4]. It may be recalled that if A is a self-adjoint operator on a Hubert space § with spectral resolution A=zf\dE\, then the set of elements x in § for which ||-Ex#|| is an absolutely continuous function of X is a subspace, &a(A), of § (see, e.g., Halmos [l, p. 104]). The op...
متن کاملSchrödinger operators with oscillating potentials ∗
Schrödinger operators H with oscillating potentials such as cos x are considered. Such potentials are not relatively compact with respect to the free Hamiltonian. But we show that they do not change the essential spectrum. Moreover we derive upper bounds for negative eigenvalue sums of H.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1984
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1984-15262-5