densely defined造句

• The notion of spectrum extends to densely defined unbounded operators.
• Note that exists if and only if is densely defined.
• Is an isometry and a densely defined homomorphism on the ring of polynomial functions.
• Some well-known properties for bounded operators generalize to closed densely defined operators.
• Hence : is the graph of some operator if and only if is densely defined.
• If is closed, densely defined and continuous on its domain, then its domain is all of.
• :( which is a densely defined " linear " map ) is a continuous linear functional.
• For instance, the last property now states that is an extension of if, and are densely defined operators.
• A densely defined, closed operator is called " normal " if it satisfies the following equivalent conditions:
• Where is a densely defined self-adjoint operator, called the system imaginary unit and is the reduced Planck constant.
• Moreover, the kernel of a closed densely defined operator coincides with the orthogonal complement of the range of the adjoint.
• *The Paley Wiener integral, on the other hand, is an example of a continuous extension of a densely defined operator.
• A densely defined linear operator on a Hilbert space is "'self-adjoint "'if it equals its adjoint.
• For any densely defined operator " A " on Hilbert space one can define its adjoint operator " A " *.
• In the model, the operator " T " is multiplication by " x " and a densely defined symmetric operator.
• A densely defined, symmetric operator " T " is essentially self-adjoint if and only if both operators, have dense range.
• For each is uniquely determined if and only if the so extended linear functional was densely defined; i . e ., if is densely defined.
• For each is uniquely determined if and only if the so extended linear functional was densely defined; i . e ., if is densely defined.
• A densely defined operator from a complex Hilbert space to itself is a linear operator whose domain is a dense linear subspace of and whose values lies in.
• A densely defined operator on a Hilbert space is called "'bounded from below "'if is a positive operator for some real number.