Spectral $$\varvec{\zeta }$$-functions and $$\varvec{\zeta }$$-regularized functional determinants for regular Sturm–Liouville operators

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Guglielmo Fucci ◽  
Fritz Gesztesy ◽  
Klaus Kirsten ◽  
Jonathan Stanfill
Keyword(s):  
Zeta Functions ◽  
Sturm Liouville ◽  
Liouville Operators

scholarly journals Partial inverse problems for quadratic differential pencils on a graph with a loop

2020 ◽  
Vol 28 (3) ◽  
pp. 449-463 ◽  
Author(s):  
Natalia P. Bondarenko ◽  
Chung-Tsun Shieh
Keyword(s):  
Inverse Problems ◽  
A Priori ◽  
Spectral Characteristics ◽  
The Other ◽  
Boundary Edge ◽  
Partial Inverse ◽  
Quadratic Pencil ◽  
Sturm Liouville ◽  
Differential Pencils ◽  
Liouville Operators

AbstractIn this paper, partial inverse problems for the quadratic pencil of Sturm–Liouville operators on a graph with a loop are studied. These problems consist in recovering the pencil coefficients on one edge of the graph (a boundary edge or the loop) from spectral characteristics, while the coefficients on the other edges are known a priori. We obtain uniqueness theorems and constructive solutions for partial inverse problems.

scholarly journals Partial inverse problems for Sturm–Liouville operators on trees

2017 ◽  
Vol 147 (5) ◽  
pp. 917-933 ◽  
Author(s):  
Natalia Bondarenko ◽  
Chung-Tsun Shieh
Keyword(s):  
Inverse Problems ◽  
A Priori ◽  
Potential Functions ◽  
Inverse Spectral Problems ◽  
Spectral Sets ◽  
Spectral Problems ◽  
Partial Inverse ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville ◽  
Liouville Operators

In this paper, inverse spectral problems for Sturm–Liouville operators on a tree (a graph without cycles) are studied. We show that if the potential on an edge is known a priori, then b – 1 spectral sets uniquely determine the potential functions on a tree with b external edges. Constructive solutions, based on the method of spectral mappings, are provided for the considered inverse problems.

scholarly journals Limiting eigenfunctions of Sturm–Liouville operators subject to a spectral flow

2020 ◽  
Author(s):  
Thomas Beck ◽  
Isabel Bors ◽  
Grace Conte ◽  
Graham Cox ◽  
Jeremy L. Marzuola
Keyword(s):  
Spectral Flow ◽  
Sturm Liouville ◽  
Liouville Operators

scholarly journals On Povzner–Wienholtz-type self-adjointness results for matrix-valued Sturm–Liouville operators

2003 ◽  
Vol 133 (4) ◽  
pp. 747-758 ◽  
Author(s):  
Steve Clark ◽  
Fritz Gesztesy
Keyword(s):  
Half Line ◽  
Sturm Liouville ◽  
Image Position ◽  
Liouville Operators

We derive Povzner–Wienholtz-type self-adjointness results for m × m matrix-valued Sturm–Liouville operators in L2((a, b);R dx)m, m ∈ N, for (a, b) a half-line or R.

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