Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval
نویسندگان
چکیده
منابع مشابه
Unbounded 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 کاملUnbounded operators and the Friedrichs extension
In this note, by A ⊂ B, I mean that A is contained in B, and it may be that A = B; usually I write this by A ⊆ B, but A ⊂ B fits with the usual notation for saying that an operator is an extension of another. In this note, unless we say otherwise H denotes a Hilbert space over C, and we do not presume H to be separable. We shall write the inner product 〈·, ·〉 on H as conjugate linear in the sec...
متن کاملAlgebraic Solving of Complex Interval Linear Systems by Limiting Factors
In this work, we propose a simple method for obtaining the algebraic solution of a complex interval linear system where coefficient matrix is a complex matrix and the right-hand-side vector is a complex interval vector. We first use a complex interval version of the Doolittle decomposition method and then we restrict the Doolittle's solution, by complex limiting factors, to achieve a complex in...
متن کاملExtension of Spectral Scales to Unbounded Operators
We extend the notion of a spectral scale to n-tuples of unbounded operators affiliated with a finite von Neumann Algebra. We focus primarily on the single-variable case and show that many of the results from the bounded theory go through in the unbounded situation. We present the currently available material on the unbounded multivariable situation. Sufficient conditions for a set to be a spect...
متن کاملSelf-adjoint, globally defined Hamiltonian operators for systems with boundaries
For a general self-adjoint Hamiltonian operator H0, defined on the Hilbert space L (IRn), we determine the set of all self-adjoint Hamiltonians H on L(IRn) that (dynamically) confine the system to an open set S ⊂ IRn while reproducing the action of H0 on an appropriate domain. We propose strategies for constructing these Hamiltonians explicitly and for n = 1 we prove that an important class amo...
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: Mathematica Bohemica
سال: 2010
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.2010.140698