Sentence examples for defined operator on a from inspiring English sources

Let T be a closed, densely defined operator on a Hilbert space H.

A type (A) family is a function, (A beta )), for (beta in Omega ), a region in ({mathbb {C}}), so that (A beta )) is a closed, densely defined operator on a Banach space, X, with domain (D(A beta )) = {mathcal {D}}) independent of (beta ) and so that for all (varphi in {mathcal {D}}) we have that (beta mapsto A beta )varphi ) is an analytic vector valued function.

P is the Helmholz-Leray orthogonal projection in ((L^{2}(Omega))^{2}) onto the space H, (A:=-PDelta) is the Stokes operator subject to the nonslip homogeneous Dirichlet boundary condition with the domain ((H^{2}(Omega))^{2}cap V), and A is a self-adjoint positively defined operator on H. (A^{-1}) is a compact operator from H to H.

In this theorem, it is understood that T is an everywhere defined operator on ℋ.

As a first step toward remedying this situation, we consider (mathfrak {q}(W)) as a space of densely defined operators on the completion (fancyscript {A}_V) (cf. Sect. 2.6.3) of the spinor oscillator module (mathfrak {a}(V)).

where, is a linear densely defined operator of sectorial type on a complex Banach space and is a pseudo-almost periodic function (see Definition 2.10) satisfying suitable conditions in.

where 1 < α < 2, A : D ( A ) ⊂ X → X is a linear densely defined operator of sectorial type on a complex Banach space X and f : R + × X → X is an appropriate function.

where A : D ( A ) = : H ˜ → H is a closed densely defined linear operator on a complex Hilbert space H, C is a bounded operator defined everywhere in L 2 ( U ; H ), ϕ ∈ L 2 ( U ; H ) and u ∈ L 2 ( U ; H ˜ ), H ˜ ⊂ H, U : = { z ∈ C : | z | < 1 }.

In classical physics an observable value is just a number; today a quantum mechanical observable value is defined as an operator on a Hilbert space.

Armed with this fact, we define an operator A on (D mathcal{T})) by Ak = Pk^{prime}, quad k^{prime}inmathcal{T}(k).

In studying the equation (Au=0), where A is a monotone operator defined on a real Hilbert space, Browder [20], introduced an operator T defined by (T:=I-A), where I is the identity mapping on H.