Some counterexamples involving selfadjoint operators
نویسندگان
چکیده
منابع مشابه
Schrödinger Operators with Decaying Potentials: Some Counterexamples
More specifically, we study the spectral properties of the associated selfadjoint operators Hβ = −d2/dx2 + V (x), acting on the Hilbert space L2(0,∞). The index β ∈ [0,π) refers to the boundary condition y(0)cosβ + y′(0)sin β = 0. For the general theory, see, for example, [29]. These questions are of relevance in quantum mechanics; for more background information on this topic, refer to, for ex...
متن کاملNon-selfadjoint Perturbations of Selfadjoint Operators in 2 Dimensions I
This is the first in a series of works devoted to small non-selfadjoint perturbations of selfadjoint h-pseudodifferential operators in dimension 2. In the present work we treat the case when the classical flow of the unperturbed part is periodic and the strength ǫ of the perturbation is ≫ h (or sometimes only ≫ h2) and bounded from above by hδ for some δ > 0. We get a complete asymptotic descri...
متن کاملSums of Regular Selfadjoint Operators
This is an unedited transscript of the handwritten notes of my talk at the Master Class.
متن کاملPairs of Selfadjoint Operators and Their Invariants
A trace formula is proved for pairs of selfadjoint operators that are close to each other in a certain sense. An important role is played by a function analytic in the open upper half-plane and with positive imaginary part there. This function, called the characteristic function of the pair, coincides with Krĕın’s Q-function in the case where the selfadjoint operators are canonical extensions o...
متن کاملSpectral perturbation bounds for selfadjoint operators I∗
We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for finite eigenvalues are obtained by using analyticity and monotonicity properties (rather than variational principles) and they are general enough to include ...
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: Rocky Mountain Journal of Mathematics
سال: 1972
ISSN: 0035-7596
DOI: 10.1216/rmj-1972-2-1-143