Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization"
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2013
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Journal of Mathematical Physics, Analysis, Geometry
2013, vol. 9, No. 2, pp. 266
Errata
Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the
Arnold Alternation Theorem and its Generalization"(Mat. Fiz. Anal. Geom., 12
(2005), No. 1, 119 � 125. (Russian))
The proof of Theorem 2 in the author's paper [1] requires partial re�nement.
Namely, the concluding part of the proof of Theorem 2, starting from the point
where the new spectral parameter µ is introduced (p. 122), is to be replaced as
follows:
With cosB = 0, Theorem 2 becomes identical to Theorem 1.1 from the mono-
graphs [2, 3]. In the general case, the proof of Theorem 2 goes similarly to that of
Theorem 1.1 from [2, 3], applying analogs of Lemmas 1.1, 1.2, and that of Theo-
rem 1.3 from [2, 3] to Y [x, λ,B] instead of Y (x, λ). Those analogs are established
under assumptions of Theorem 2 with formula (14) from [1] applied to ha. Here
ha is a self-adjoint operator in the closure of its domain D(ha). Suitable analogs
of Lemmas 1.1, 1.2, and that of Theorem 1.3 from [2, 3], under assumptions of
Theorem 2 for ha, have been established, after the author's hint, by A.M. Kholkin.
With this re�ned proof, the formulation of Theorem 2 from [1] remains intact.
(See also Proposition 1.1 of [3], p. 4).
References
[1] F.S. Rofe-Beketov, Operator-Theoretical Proof of the Arnold Alternation The-
orem and its Generalization. � Mat. Fiz. Anal. Geom. 12 (2005), No. 1,
119�125. (Russian)
[2] F.S. Rofe-Beketov and A.M. Kholkin, Spectral Analysis of Di�erential Ope-
rators. A Relation Between Spectral and Oscillatory Properties. 332, PSTU,
Mariupol, 2001. (Russian)
[3] F.S. Rofe-Beketov and A.M. Kholkin, Spectral Analysis of Di�erential Ope-
rators. Interplay Between Spectral and Oscillatory Properties. xxiii+438 pp.,
World Scienti�c, New Jersey-London-Singapore-Beijing-Shanghai-Hong Kong-
Taipei-Chennai, 2005.
266
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irk-123456789-1067492016-10-05T03:02:06Z Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization" 2013 Article Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization" // Журнал математической физики, анализа, геометрии. — 2013. — Т. 9, № 2. — С. 266. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106749 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| format |
Article |
| title |
Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization" |
| spellingShingle |
Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization" Журнал математической физики, анализа, геометрии |
| title_short |
Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization" |
| title_full |
Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization" |
| title_fullStr |
Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization" |
| title_full_unstemmed |
Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization" |
| title_sort |
erratum to the paper f.s. rofe-beketov "operator-theoretical proof of the arnold alternation theorem and its generalization" |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106749 |
| citation_txt |
Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization" // Журнал математической физики, анализа, геометрии. — 2013. — Т. 9, № 2. — С. 266. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| first_indexed |
2025-07-07T18:56:34Z |
| last_indexed |
2025-07-07T18:56:34Z |
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1837015598451654656 |