منابع مشابه
Positive Perturbations of Unbounded Operators
This work studies the spectral properties of certain unbounded selfadjoint operators by considering positive perturbations of such operators and the unitary equivalence of the perturbed and unperturbed transformations. Conditions are obtained on the unitary operators implementing this equivalence which guarantee that the selfadjoint operators have an absolutely continuous part.
متن کاملUnbounded operators, Friedrichs’ extension theorem
Explicit naming of the domain of an unbounded operator is often suppressed, instead writing T1 ⊂ T2 when T2 is an extension of T1, in the sense that the domain of T2 contains that of T1, and the restriction of T2 to the domain of T1 agrees with T1. An operator T ′, D′ is a sub-adjoint to an operator T,D when 〈Tv,w〉 = 〈v, T ′w〉 (for v ∈ D, w ∈ D′) For D dense, for given D′ there is at most one T...
متن کاملOn unbounded operators and applications
is a solvable linear equation in a Hilbert space H , A is a linear, closed, densely defined, unbounded operator in H , which is not boundedly invertible, so problem (1) is ill-posed. It is proved that the closure of the operator (AA + α I )−1A∗, with the domain D(A), where α > 0 is a constant, is a linear bounded everywhere defined operator with norm ≤ 1 2 √ α . This result is applied to the va...
متن کاملDifferentiable Perturbation of Unbounded Operators
If A(t) is a C1,α-curve of unbounded self-adjoint operators with compact resolvents and common domain of definition, then the eigenvalues can be parameterized C1 in t. If A is C∞ then the eigenvalues can be parameterized twice differentiable. Theorem. Let t 7→ A(t) for t ∈ R be a curve of unbounded self-adjoint operators in a Hilbert space with common domain of definition and with compact resol...
متن کاملExponential splitting for unbounded operators
We present a convergence analysis for exponential splitting methods applied to linear evolution equations. Our main result states that the classical order of the splitting method is retained in a setting of unbounded operators, without requiring any additional order condition. This is achieved by basing the analysis on the abstract framework of (semi)groups. The convergence analysis also includ...
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: Integral Equations and Operator Theory
سال: 2014
ISSN: 0378-620X,1420-8989
DOI: 10.1007/s00020-014-2133-1