Sentence examples for operator in the case from inspiring English sources

Fortunately, we can prove the continuity of a resolvent in the uniform operator topology and the compactness of the solution operator in the case of an analytic resolvent.

It is proven that the Euler characteristic of the graph can be calculated from the spectrum of the Schrödinger operator in the case of essentially bounded real potentials and standard boundary conditions at the vertices.

By Theorem 6.1 in [12], each self-adjoint subspace extension (H_{1}) of (H_{0}) is a self-adjoint operator in the case that (I= -infty, +I= -inftythat is, (H_{1}) can define a single-valued self-adjoint operator in (l_{w}^{2}(-infty,+infty)) whose graph is (H_{1}).

Recently, Gupta and Wang [3] proposed certain q-Durrmeyer operators in the case of real variables.

In the following lemma, Tanahashi, Jeon, Kim, and Uchiyama extended the result (1.3) to -quasiclass A operators in the case.

Remark 2 Recently, it is much more interesting to study these operators in the case q > 1. Authors continue to study that case.

For non-decreasing operators, in the case of an upper solution, it was proved in [4] the following result which is an improvement of those in [2, 3].

In this paper, we establish some existence results of φ-fixed points for various classes of operators in the case, where X is endowed with a metric d.

Parking charges are determined by the local authorities, where the parking lots are city property, or by the private operators in the case of private parking facilities.

The problem (2.1), (2.2) is studied for the Riemann-Liouville and Caputo operators in the case of the Laplace equation, i.e., when g ( x ) = 0, in the same works [8, 9].

Some of the inequalities in Corollary 3.3 can be used to produce reverse norm inequalities for the sum of positive operators in the case when the convex function is nonnegative and monotonic nondecreasing on.