I. M. Karabash, A. S. Kostenko, “Similarity of $\operatorname{sgn}x\bigl(-\frac{d^2}{dx^2}+c\delta\bigr)$ Type Operators to Normal and Self-adjoint Operators”, Mat. Zametki, 74:1 (2003), 134–139; Math. Notes, 74:1 (2003), 127

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Matematicheskie Zametki, 2003, Volume 74, Issue 1, Pages 134–139
DOI: https://doi.org/10.4213/mzm585 (Mi mzm585)

This article is cited in 13 scientific papers (total in 13 papers)

Brief Communications

Similarity of

sgn x (- \frac{d^{2}}{d x^{2}} + c δ)

$\operatorname{sgn}x\bigl(-\frac{d^2}{dx^2}+c\delta\bigr)$ Type Operators to Normal and Self-adjoint Operators

I. M. Karabash, A. S. Kostenko

Donetsk National University

Full-text PDF (227 kB) Citations (13)

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DOI: https://doi.org/10.4213/mzm585

Received: 12.11.2002

English version:
Mathematical Notes, 2003, Volume 74, Issue 1, Pages 127–131
DOI: https://doi.org/10.1023/A:1025031519433

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: I. M. Karabash, A. S. Kostenko, “Similarity of

sgn x (- \frac{d^{2}}{d x^{2}} + c δ)

$\operatorname{sgn}x\bigl(-\frac{d^2}{dx^2}+c\delta\bigr)$ Type Operators to Normal and Self-adjoint Operators”, Mat. Zametki, 74:1 (2003), 134–139; Math. Notes, 74:1 (2003), 127–131

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm585

https://doi.org/10.4213/mzm585

https://www.mathnet.ru/eng/mzm/v74/i1/p134

This publication is cited in the following 13 articles:

Branko Ćurgus, Volodymyr Derkach, Carsten Trunk, “Indefinite Sturm–Liouville Operators in Polar Form”, Integr. Equ. Oper. Theory, 96:1 (2024)
Aharonov Ya., Behrndt J., Colombo F., Schlosser P., “Green'S Function For the Schrodinger Equation With a Generalized Point Interaction and Stability of Superoscillations”, J. Differ. Equ., 277 (2021), 153–190
Gimaltdinova A., “The Dirichlet Problem For An Equation of Mixed Type With Two Internal Lines of Type Change”, Lobachevskii J. Math., 41:11, SI (2020), 2155–2167
Krejcirik D. Siegl P. Zelezny J., “On the Similarity of Sturm-Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators”, Complex Anal. Oper. Theory, 8:1 (2014), 255–281
Markov V.G., “Nekotorye svoistva neznakoopredelennykh operatorov shturma-liuvillya”, Matematicheskie zametki YaGU, 19:1 (2012), 44–59
Karabash I.M., “A Functional Model, Eigenvalues, and Finite Singular Critical Points for Indefinite Sturm-Liouville Operators”, Topics in Operator Theory, Vol 2: Systems and Mathematical Physics, Operator Theory Advances and Applications, 203, eds. Ball J., Bolotnikov V., Helton J., Rodman L., Spitkovsky I., Birkhauser Verlag Ag, 2010, 247–287
Behrndt J., “On the spectral theory of singular indefinite Sturm-Liouville operators”, J. Math. Anal. Appl., 334:2 (2007), 1439–1449
Behrndt J., Trunk C., “On the negative squares of indefinite Sturm-Liouville operators”, J. Differential Equations, 238:2 (2007), 491–519
Karabash I. Kostenko A., “Spectral Analysis of Differential Operators with Indefinite Weights and a Local Point Interaction”, Operator Theory in Inner Product Spaces, Operator Theory : Advances and Applications, 175, ed. Forster KH. Jones P. Langer H. Trunk C., Birkhauser Verlag Ag, 2007, 169–191
A. S. Kostenko, “Similarity of Some $J$ -Nonnegative Operators to Self-Adjoint Operators”, Math. Notes, 80:1 (2006), 131–135
Kostenko A.S., “Spectral Analysis of Some Indefinite Sturm-Liouville Operators”, Operator Theory 20, Proceedings, ed. Davidson K. Gaspar D. Stratila S. Timotin D. Vasilescu F., Theta Foundation, 2006, 131–141
Albeverio S., Kuzhel S., “One-dimensional Schrödinger operators with $\mathscr P$ -symmetric zero-range potentials”, J. Phys. A, 38:22 (2005), 4975–4988
A. S. Kostenko, “Similarity of Indefinite Sturm–Liouville Operators with Singular Potential to a Self-Adjoint Operator”, Math. Notes, 78:1 (2005), 134–139

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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