unbounded operator造句

• The notion of spectrum extends to densely defined unbounded operators.
• Differential operators are an important class of unbounded operators.
• See also Extensions of symmetric operators and unbounded operator.
• Just find any linearly independent sequence and make an unbounded operator on it.
• A generalization of Douglas'lemma for unbounded operators on a Banach space is given in.
• Because the axioms are dealing with unbounded operators, the domains of the operators have to be specified.
• As Connes showed, these spaces can be realised as unbounded operators only by using a certain positive power of the reference modular operator.
• For technical reasons, one needs to consider separately the positive and negative parts of " A " defined by the Borel functional calculus for unbounded operators.
• This is similar to Dirac's formulation of quantum mechanics, though Dirac also allowed unbounded operators, and did not distinguish clearly between self-adjoint and Hermitian operators.
• When Heisenberg was informed von Neumann had clarified the difference between an unbounded operator that was a self-adjoint operator and one that was merely symmetric, Heisenberg replied " Eh?
• The term " operator " often means " bounded linear operator ", but in the context of this article it means " unbounded operator ", with the reservations made above.
• The short proof given above was first published by Rosenblum in 1958; it is very elegant, but is less general than the original proof which also considered the case of unbounded operators.
• For the proof to make sense, the vector \ hat { B } | \ Psi \ rangle has to be in the domain of the unbounded operator \ hat { A }, which is not always the case.
• One can extend the definition of spectrum for unbounded operators on a Banach space " X ", operators which are no longer elements in the Banach algebra " B " ( " X " ).
• Similar considerations apply to the eigenstates of the momentum operator, or indeed any other self-adjoint unbounded operator " P " on the Hilbert space, provided the spectrum of " P " is continuous and there are no degenerate eigenvalues.
• Combined with suitable boundary conditions and expressed on a suitable Banach space " X " ( which encodes both the boundary conditions and the desired regularity of the solution ), " L " becomes an unbounded operator from " X " to itself, and one attempts to solve