On extensions of symmetric operators

Guliyev, Namig J.

doi:10.7153/oam-2020-14-05

Cited by 3 publications

(1 citation statement)

References 12 publications

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“…This kind of linearization procedure goes back at least to a 1956 book by Friedman [2, pp. 205-207] and can even be generalized to arbitrary (not necessarily rational) Herglotz-Nevanlinna functions [8].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

A Riesz basis criterion for Schrödinger operators with boundary conditions dependent on the eigenvalue parameter

Guliyev

2019

Anal.Math.Phys.

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We establish a criterion for a set of eigenfunctions of the onedimensional Schrödinger operator with distributional potentials and boundary conditions containing the eigenvalue parameter to be a Riesz basis for L 2 (0, π).2010 Mathematics Subject Classification. 42C15, 42C30, 15B05, 34B07, 34L10, 34L40, 46B15, 46C05, 46E30, 47A20, 47B25, 47E05.Key words and phrases. Riesz basis, one-dimensional Schrödinger equation, distributional potential, Sturm-Liouville operator, singular potential, boundary conditions dependent on the eigenvalue parameter.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

A Riesz basis criterion for Schrödinger operators with boundary conditions dependent on the eigenvalue parameter

Guliyev

2019

Anal.Math.Phys.

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On two-spectra inverse problems

Guliyev

2020

Proc. Amer. Math. Soc.

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Inverse square singularities and eigenparameter-dependent boundary conditions are two sides of the same coin

Guliyev¹

2023

The Quarterly Journal of Mathematics

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We show that inverse square singularities can be treated as boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenvalue parameter with ‘a negative number of poles’. More precisely, we treat in a unified manner one-dimensional Schrödinger operators with either an inverse square singularity or a boundary condition containing a rational Herglotz–Nevanlinna function of the eigenvalue parameter at each endpoint and define Darboux-type transformations between such operators. These transformations allow one, in particular, to transfer almost any spectral result from boundary value problems with eigenparameter-dependent boundary conditions to those with inverse square singularities and vice versa.

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On extensions of symmetric operators

Abstract: We give an explicit description of all minimal self-adjoint extensions of a densely defined, closed symmetric operator in a Hilbert space with deficiency indices (1, 1).2010 Mathematics Subject Classification. 47A20, 47B25.

Cited by 3 publications

References 12 publications

A Riesz basis criterion for Schrödinger operators with boundary conditions dependent on the eigenvalue parameter

A Riesz basis criterion for Schrödinger operators with boundary conditions dependent on the eigenvalue parameter

On two-spectra inverse problems

Inverse square singularities and eigenparameter-dependent boundary conditions are two sides of the same coin

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