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arXiv · 2109.04679

The positive and negative deficiency indices of formally self-adjoint difference equations

Guojing Ren
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Abstract

This paper is concerned with formally self-adjoint difference equations and their positive and negative deficiency indices. It is shown that the order of any formally self-adjoint difference equation is even, and some characterizations of formally self-adjoint difference equations are established. Further, we show that the positive and negative deficiency indices are always equal, which implies the existence of the self-adjoint extensions of the minimal linear relations generated by the difference equations. This is an important and essential difference between formally self-adjoint difference equations and their corresponding differential equations in the spectral theory.

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Guojing Ren. 2021-09-10. The positive and negative deficiency indices of formally self-adjoint difference equations. https://arxiv.org/abs/2109.04679

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