Inverse problems for differential operators of variable orders on star-type graphs: general case

Yurko, V. A.

doi:10.1007/s13324-014-0068-y

Cited by 4 publications

(4 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such equations appear in various problems of mathematics and in applications (see, for example, [47] and the bibliography therein), for example, for describing oscillations in such structures as masts with cable supports, cable-stayed bridges and others. Some results on inverse problems for variable order differential operators were obtained in [48][49][50][51][52]. These results are presented in subsections 4.2, 4.3, 5.4 of the present review.…”

Section: Introductionmentioning

confidence: 89%

“…Such problems are studied only recently, and nowadays they are investigated insufficiently. In [48][49][50] inverse spectral problems are considered for variable order operators on compact graphs (see also subsections 4.2 and 4.3 of the present paper). In this subsection, in contrast to the works [48][49][50], we study the inverse spectral problem on a noncompact graph.…”

Section: Variable Order Operators On a Noncompact With A Cyclementioning

confidence: 99%

“…In [48][49][50] inverse spectral problems are considered for variable order operators on compact graphs (see also subsections 4.2 and 4.3 of the present paper). In this subsection, in contrast to the works [48][49][50], we study the inverse spectral problem on a noncompact graph. The graph consists of a cycle and a ray with a common vertex.…”

Section: Variable Order Operators On a Noncompact With A Cyclementioning

confidence: 99%

See 2 more Smart Citations

Uniqueness of Recovering Arbitrary Order Differential Operators on Noncompact Spatial Networks

Yurko¹

2012

MMI

View full text Add to dashboard Cite

We give a short review of results on inverse spectral problems for ordinary differential operators on a spatial networks (geometrical graphs). We pay the main attention to the most important nonlinear inverse problems of recovering coefficients of differential equations from spectral characteristics provided that the structure of the graph is known a priori. In the first half of the review we provide results related to inverse Sturm-Liouville problems on arbitrary compact graphs. Further, results on inverse problems for arbitrary order differential operators on compact graphs are presented. At the end we provide the main results on inverse problems on noncompact graphs.Bibliography: 55 titles.

show abstract

Section: Introductionmentioning

confidence: 89%

Section: Variable Order Operators On a Noncompact With A Cyclementioning

confidence: 99%

Section: Variable Order Operators On a Noncompact With A Cyclementioning

confidence: 99%

See 1 more Smart Citation

Uniqueness of Recovering Arbitrary Order Differential Operators on Noncompact Spatial Networks

Yurko¹

2012

MMI

View full text Add to dashboard Cite

show abstract

“…This provides general forms for the representation of the resolvent as an integral operator and for a spectral representation. The representation of the resolvent as an integral operator, m functions, and spectral representations for operators on graphs have appeared in many, more specific situations [1], [2], [3], [5], [8], [10], [11]- [13], [15], [19], [21], [25], [27], [30].…”

Section: Introductionmentioning

confidence: 99%

Canonical systems and quantum graphs

Scarbrough¹

2021

Preprint

View full text Add to dashboard Cite

The representation of the resolvent as an integral operator, the m function, and the associated spectral representation are fundamental topics in the spectral theory of self-adjoint ordinary differential operators. Versions of these are developed here for canonical systems Ju ′ = −zHu of arbitrary order. A classical result shows that canonical systems of order two can be used to realize arbitrary spectral data, in the form of m functions from the upper half plane to itself. In this paper, canonical systems on graphs, not necessarily compact but with finitely many vertices, are introduced and proved to be unitarily equivalent to certain higher order canonical systems. It is shown that any Schrödinger operator on a graph is unitarily equivalent to a canonical system on the same graph. Consequently, for an arbitrary canonical system or Schrödinger operator on a graph, a representation of the resolvent as an integral operator and a spectral representation are obtained.

show abstract

Inverse spectral problems for differential operators on spatial networks

Yurko¹

2016

Russ. Math. Surv.

View full text Add to dashboard Cite

Inverse problems for differential operators of variable orders on star-type graphs: general case

Cited by 4 publications

References 20 publications

Uniqueness of Recovering Arbitrary Order Differential Operators on Noncompact Spatial Networks

Uniqueness of Recovering Arbitrary Order Differential Operators on Noncompact Spatial Networks

Canonical systems and quantum graphs

Inverse spectral problems for differential operators on spatial networks

Contact Info

Product

Resources

About