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We start by discussing matrix operators on closed manifolds.

In [21] they have characterized some matrix operators on these spaces by applying the Hausdorff measure of noncompactness.

In this section, we derive some identities or estimates for the Hausdorff measures of noncompactness of certain matrix operators on the spaces of generalized means.

In this work, we establish identities or estimates for the operator norms and the Hausdorff measure of noncompactness of certain matrix operators on these spaces that were defined by Ozger and Basar in [16].

In this paper, we derive some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the sequence space (ell_{p}(r,s,t B^{(m)})).

In this paper, we have derived some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the sequence space (ell_{p}(r,s,t B^{(m)})).

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The paper presents a new general theory of interaction of eigenvalues of matrix operators depending on parameters.

In [5] it was shown that the norm of the Hilbert matrix operator H on the Bergman space Ap is equal to πsin2πp, when 4≤p<∞, and it was also conjectured that‖H‖Ap→Ap="πsin⁡2πp, when 2

The resulting equations are discretized on time domain using a set of time differential matrix operators that are defined based on the derivatives of a periodic base function.

In the next step, the time domain is discretized via spectral differentiation matrix operators which are defined based on the derivatives of a periodic base function.

On the other hand, the RHS of conventional ADI-FDTD still involves matrix operators A and B, c.f. Eq. (16).

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