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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年11月28日

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  • Christoph Fischbacher,
  • Fritz Gesztesy,
  • Lance L. Littlejohn

摘要

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.