Limit‐point/limit‐circle classification for Hain–Lüst type equations

Hassi, Seppo; Möller, Manfred; Snoo, Henk de

doi:10.1002/mana.201600254

Cited by 4 publications

(1 citation statement)

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“…Under certain circumstances the Weyl function in the limit-point case (of a usual Sturm-Liouville operator) belongs to the Kac class; see for instance [420]. For further results in this direction, see [384,385,386,387]; in these cases there is a distinguished selfadjoint extension, namely the generalized Friedrichs extension; see the notes on Chapter 5. Sturm-Liouville equations with vector-valued coefficients are beyond the scope of this text; see [345,346] and for a recent contribution [330].…”

Section: Notes On Chaptermentioning

confidence: 99%

Boundary Value Problems, Weyl Functions, and Differential Operators

Behrndt

Hassi

Snoo

2020

Monographs in Mathematics

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The foundations of this outstanding book series were laid in 1944. Until the end of the 1970s, a total of 77 volumes appeared, including works of such distinguished mathematicians as Carathéodory, Nevanlinna and Shafarevich, to name a few. The series came to its name and present appearance in the 1980s. In keeping its well-established tradition, only monographs of excellent quality are published in this collection. Comprehensive, in-depth treatments of areas of current interest are presented to a readership ranging from graduate students to professional mathematicians. Concrete examples and applications both within and beyond the immediate domain of mathematics illustrate the import and consequences of the theory under discussion.

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Section: Notes On Chaptermentioning

confidence: 99%

Boundary Value Problems, Weyl Functions, and Differential Operators

Behrndt

Hassi

Snoo

2020

Monographs in Mathematics

Self Cite

147

227

View full text Add to dashboard Cite

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On classification of singular matrix difference equations of mixed order

Sun²,

Xie³

2023

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar classical Weyl's method by selecting a suitable quasi-difference. An equivalent characterization of this classification is given in terms of the number of linearly independent square summable solutions of the equation. The influence of off-diagonal coefficients on the classification is illustrated by two examples. In particular, two limit point criteria are established in terms of coefficients of the equation.

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Analysis of azimuthal magnetorotational instability of rotating magnetohydrodynamic flows and Tayler instability via an extended Hain-Lüst equation

et al. 2020

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Short-wavelength local analysis and numerical global analysis are made of the azimuthal magnetorotational instability of rotating flows of an electrically conducting fluid, subject to an arbitrary but axisymmetric azimuthal magnetic field, to three-dimensional disturbances. We extend the Hain-Lüst equation for the radial Lagrangian displacements by incorporating the effect of the viscosity and electrical resistivity and apply the Wentzel-Kramers-Brillouin method to it. We confirm that in the inductionless limit, in which the magnetic diffusivity is much larger than the viscosity, rotating flows with radial distributions of the angular velocity beyond the Liu limit, become unstable subject to a wide variety of the azimuthal magnetic fields, and so is the Keplerian flow. Our results compare well with the numerical global stability analysis.

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Limit‐point/limit‐circle classification for Hain–Lüst type equations

Cited by 4 publications

References 45 publications

Boundary Value Problems, Weyl Functions, and Differential Operators

Boundary Value Problems, Weyl Functions, and Differential Operators

On classification of singular matrix difference equations of mixed order

Analysis of azimuthal magnetorotational instability of rotating magnetohydrodynamic flows and Tayler instability via an extended Hain-Lüst equation

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