Geodesic
The Sturm-Liouville Friedrichs extension
Applications of Mathematics, Tome 60 (2015) no. 3, pp. 299-320

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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.
DOI : 10.1007/s10492-015-0097-3
Classification : 34B05, 34L05, 47B25
Keywords: Sturm-Liouville operator; Friedrichs extension 
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Yao, Siqin; Sun, Jiong; Zettl, Anton. The Sturm-Liouville Friedrichs extension. Applications of Mathematics, Tome 60 (2015) no. 3, pp. 299-320. doi: 10.1007/s10492-015-0097-3

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