Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization"
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| Опубліковано в: : | Журнал математической физики, анализа, геометрии |
|---|---|
| Дата: | 2013 |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2013
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/106749 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860226369589346304 |
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| 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| first_indexed | 2025-12-07T18:20:08Z |
| format | Article |
| fulltext |
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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| id | nasplib_isofts_kiev_ua-123456789-106749 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T18:20:08Z |
| publishDate | 2013 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | 2016-10-04T17:22:32Z 2016-10-04T17:22:32Z 2013 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 https://nasplib.isofts.kiev.ua/handle/123456789/106749 en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization" Article published earlier |
| spellingShingle | Erratum to the paper F.S. Rofe-Beketov "Operator-Theoretical Proof of the Arnold Alternation Theorem and its Generalization" |
| title | 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_short | 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" |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106749 |