The Sturm-Liouville Friedrichs extension

Siqin Yao; Jiong Sun; Anton Zettl

Applications of Mathematics (2015)

  • Volume: 60, Issue: 3, page 299-320
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Yao, Siqin, Sun, Jiong, and Zettl, Anton. "The Sturm-Liouville Friedrichs extension." Applications of Mathematics 60.3 (2015): 299-320. <http://eudml.org/doc/270094>.

@article{Yao2015,
abstract = {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.},
author = {Yao, Siqin, Sun, Jiong, Zettl, Anton},
journal = {Applications of Mathematics},
keywords = {Sturm-Liouville operator; Friedrichs extension; Sturm-Liouville operator; Friedrichs extension},
language = {eng},
number = {3},
pages = {299-320},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Sturm-Liouville Friedrichs extension},
url = {http://eudml.org/doc/270094},
volume = {60},
year = {2015},
}

TY - JOUR
AU - Yao, Siqin
AU - Sun, Jiong
AU - Zettl, Anton
TI - The Sturm-Liouville Friedrichs extension
JO - Applications of Mathematics
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 3
SP - 299
EP - 320
AB - 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.
LA - eng
KW - Sturm-Liouville operator; Friedrichs extension; Sturm-Liouville operator; Friedrichs extension
UR - http://eudml.org/doc/270094
ER -

References

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  2. Friedrichs, K., 10.1007/BF01565401, Math. Ann. German 112 (1936), 1-23. (1936) MR1513033DOI10.1007/BF01565401
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  9. Naimark, M. A., Linear Differential Operators. Part II: Linear Differential Operators in Hilbert Space, Frederick Ungar Publishing, New York (1968). (1968) Zbl0227.34020MR0262880
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  13. Rosenberger, R., Characterization of the Friedrichs extension of semi-bounded Sturm-Liouville operators, Fachbereich Mathematik der Technischen Hochschule Darmstadt Dissertation (1984), German. (1984) Zbl0676.47027
  14. Wang, A., Sun, J., Zettl, A., Characterization of domains of self-adjoint ordinary differential operators, J. Differ. Equations (2009), 246 1600-1622. (2009) Zbl1169.47033MR2488698
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  16. Zettl, A., Sturm-Liouville Theory, Mathematical Surveys and Monographs 121 American Mathematical Society, Providence (2005). (2005) Zbl1103.34001MR2170950

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