The Sturm-Liouville Friedrichs extension

[摘要] The characterization of the domain of the Friedrichs extension as a restriction of the maximal domain is well known. It depends on principal solutions. Here we establish a characterization as an extension of the minimal domain. Our proof is different and closer in spirit to the Friedrichs construction. It starts with the assumption that the minimal operator is bounded below and does not directly use oscillation theory.

[学科分类] 应用数学

[关键词] Sturm-Liouville operator;Friedrichs extension