# On Maximal Regularity of Differential and Difference Operators

Conference paper

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## Abstract

In this paper we investigate a linear degenerate second-order difference operator and we find conditions that are sufficient for its bounded invertibility and separability in Hilbert space. We apply these results to prove the solvability of an infinite quasilinear difference system. We also give one result on the separability of its continuous analogue (a degenerate differential operator of second order) and show that the second-order discrete operator is separable under much weaker conditions.

## Notes

### Acknowledgement

This research was supported by the grant AP05131649 of the Ministry of Education and Science of the Republic of Kazakhstan.

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