Self-adjoint subspace extensions of nondensely defined symmetric operators
نویسندگان
چکیده
منابع مشابه
Commuting Self-Adjoint Extensions of Symmetric Operators Defined from the Partial Derivatives
We consider the problem of finding commuting self-adjoint extensions of the partial derivatives { 1 i ∂ ∂xj : j = 1, . . . , d } with domain C c (Ω) where the self-adjointness is defined relative to L (Ω), and Ω is a given open subset of R. The measure on Ω is Lebesgue measure on R restricted to Ω. The problem originates with I.E. Segal and B. Fuglede, and is difficult in general. In this paper...
متن کاملComplex Powers of Nondensely Defined Operators
The power (−A)b, b ∈ C is defined for a closed linear operator A whose resolvent is polynomially bounded on the region which is, in general, strictly contained in an acute angle. It is proved that all structural properties of complex powers of densely defined operators with polynomially bounded resolvent remain true in the newly arisen situation. The fractional powers are considered as generato...
متن کاملSelf Adjoint Extensions of Phase and Time Operators
It is shown that any real and even function of the phase (time) operator has a self-adjoint extension and its relation to the general phase operator problem is analyzed. Typeset using REVTEX E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]
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 کاملSelf-adjoint Difference Operators and Symmetric Al-salam–chihara Polynomials
The symmetric Al-Salam–Chihara polynomials for q > 1 are associated with an indeterminate moment problem. There is a self-adjoint second order difference operator on l(Z) to which these polynomials are eigenfunctions. We determine the spectral decomposition of this self-adjoint operator. This leads to a class of discrete orthogonality measures, which have been obtained previously by Christianse...
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: Advances in Mathematics
سال: 1974
ISSN: 0001-8708
DOI: 10.1016/0001-8708(74)90034-6