Sentence examples for a compact inverse from inspiring English sources

Observe that has a compact inverse.

where A is a self-adjoint positive-definite operator in H which has a compact inverse operator and A > E (E is an identity operator in H).

Now, consider the equation: (2) (3). in L2 (H, [0, 1]), where A is a self-adjoint positive-definite operator in H which has a compact inverse operator.

According to the eigenvalue theory of elliptic operators, the Laplacian on with the Neumann boundary conditions is a self-adjoint operator with compact inverse, so there exists a sequence of nonnegative eigenvalues (going to ) and a sequence of corresponding eigenfunctions, which are denoted by and, respectively.

Since (mathcal{A}_{0}) is a self-adjoint positive operator with compact inverse, ({omega_{j}}_{j=1}^{infty}) forms a basis of the space (mathbb{H}).

and where is Laplace operators and is a self-adjoint positive operators with compact inverse.

Furthermore, we study problem (1.1) without assuming that B has bounded (or compact) inverse and without any assumption on the relation between (D(A)) and (D(B)).

These rigorous 3D schemes can generate smooth or focused (compact) inverse images (depending primarily upon the particular objective of the interpretation) by incorporating the appropriate type of the stabilizer in the objective functional subject to minimization.

A compact X-ray source based on inverse Compton scattering of a high-power laser on a high-brightness linac beam is described.

A compact surface detector designed to identify the inverse beta decay interaction produced by anti-neutrinos coming from near operating nuclear reactors is being developed by the Neutrinos Angra Collaboration.

It is a classic inverse problem which consists of achieving a compact region-based description of the image scene by decomposing it into meaningful or spatially coherent regions sharing similar attributes.