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arXiv · 2504.06506

Some Remarks on the Product Formula for Defect Numbers of Closed Operators

Christoph Fischbacher·Fritz Gesztesy·Lance L. Littlejohn
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Abstract

This largely pedagogical paper recalls some facts on defect numbers of products of closed operators employing results from the theory of semi-Fredholm operators and then applies these facts to positive integer powers of symmetric operators and subsequently to certain minimal Sturm--Liouville and minimal higher even-order ordinary and partial differential operators. We also point out some unexpected missed opportunities when comparing the work of different groups on this subject.

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Christoph Fischbacher, Fritz Gesztesy, Lance L. Littlejohn. 2025-04-09. Some Remarks on the Product Formula for Defect Numbers of Closed Operators. https://arxiv.org/abs/2504.06506

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