Inverse problems on star-type graphs: differential operators of different orders on different edges

Vyacheslav Yurko

Open Mathematics (2014)

  • Volume: 12, Issue: 3, page 483-499
  • ISSN: 2391-5455

Abstract

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We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.

How to cite

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Vyacheslav Yurko. "Inverse problems on star-type graphs: differential operators of different orders on different edges." Open Mathematics 12.3 (2014): 483-499. <http://eudml.org/doc/269745>.

@article{VyacheslavYurko2014,
abstract = {We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.},
author = {Vyacheslav Yurko},
journal = {Open Mathematics},
keywords = {Geometrical graphs; Differential operators; Inverse spectral problems; Weyl-type matrices; inverse spectral problems; differential operators on graphs; Weyl function},
language = {eng},
number = {3},
pages = {483-499},
title = {Inverse problems on star-type graphs: differential operators of different orders on different edges},
url = {http://eudml.org/doc/269745},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Vyacheslav Yurko
TI - Inverse problems on star-type graphs: differential operators of different orders on different edges
JO - Open Mathematics
PY - 2014
VL - 12
IS - 3
SP - 483
EP - 499
AB - We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.
LA - eng
KW - Geometrical graphs; Differential operators; Inverse spectral problems; Weyl-type matrices; inverse spectral problems; differential operators on graphs; Weyl function
UR - http://eudml.org/doc/269745
ER -

References

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