The Integration of Double-Infinite Toda Lattice by Means of Inverse Spectral Problem and Related Quetions
The solution of the Cauchy problem for differential-difference double-infinite Toda lattice by means of inverse spectral problem for semi-infinite block Jacobi matrix is given. Namely, we construct a simple linear system of three differential equations of first order whose solution gives the spectra...
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| Date: | 2009 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/5711 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The integration of double-infinite Toda lattice by means of inverse spectral problem and related questions / Yu. Berezansky // Methods of Functional Analysis and Topology. — 2009. — Т. 15, № 2. — С. 101-136. — Бібліогр.: 48 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862735132448784384 |
|---|---|
| author | Berezansky, Yu. |
| author_facet | Berezansky, Yu. |
| citation_txt | The integration of double-infinite Toda lattice by means of inverse spectral problem and related questions / Yu. Berezansky // Methods of Functional Analysis and Topology. — 2009. — Т. 15, № 2. — С. 101-136. — Бібліогр.: 48 назв. — англ. |
| collection | DSpace DC |
| description | The solution of the Cauchy problem for differential-difference double-infinite Toda lattice by means of inverse spectral problem for semi-infinite block Jacobi matrix is given. Namely, we construct a simple linear system of three differential equations of first order whose solution gives the spectral matrix measure of the aforementioned Jacobi matrix. The solution of the Cauchy problem for the Toda lattice is given by the procedure of orthogonalization w.r.t. this spectral measure, i.e. by the solution of the inverse spectral problem for this Jacobi matrix.
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| first_indexed | 2025-12-07T19:46:41Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-5711 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1029-3531 |
| language | English |
| last_indexed | 2025-12-07T19:46:41Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Berezansky, Yu. 2010-02-02T13:43:04Z 2010-02-02T13:43:04Z 2009 The integration of double-infinite Toda lattice by means of inverse spectral problem and related questions / Yu. Berezansky // Methods of Functional Analysis and Topology. — 2009. — Т. 15, № 2. — С. 101-136. — Бібліогр.: 48 назв. — англ. 1029-3531 https://nasplib.isofts.kiev.ua/handle/123456789/5711 The solution of the Cauchy problem for differential-difference double-infinite Toda lattice by means of inverse spectral problem for semi-infinite block Jacobi matrix is given. Namely, we construct a simple linear system of three differential equations of first order whose solution gives the spectral matrix measure of the aforementioned Jacobi matrix. The solution of the Cauchy problem for the Toda lattice is given by the procedure of orthogonalization w.r.t. this spectral measure, i.e. by the solution of the inverse spectral problem for this Jacobi matrix. en Інститут математики НАН України The Integration of Double-Infinite Toda Lattice by Means of Inverse Spectral Problem and Related Quetions Article published earlier |
| spellingShingle | The Integration of Double-Infinite Toda Lattice by Means of Inverse Spectral Problem and Related Quetions Berezansky, Yu. |
| title | The Integration of Double-Infinite Toda Lattice by Means of Inverse Spectral Problem and Related Quetions |
| title_full | The Integration of Double-Infinite Toda Lattice by Means of Inverse Spectral Problem and Related Quetions |
| title_fullStr | The Integration of Double-Infinite Toda Lattice by Means of Inverse Spectral Problem and Related Quetions |
| title_full_unstemmed | The Integration of Double-Infinite Toda Lattice by Means of Inverse Spectral Problem and Related Quetions |
| title_short | The Integration of Double-Infinite Toda Lattice by Means of Inverse Spectral Problem and Related Quetions |
| title_sort | integration of double-infinite toda lattice by means of inverse spectral problem and related quetions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/5711 |
| work_keys_str_mv | AT berezanskyyu theintegrationofdoubleinfinitetodalatticebymeansofinversespectralproblemandrelatedquetions AT berezanskyyu integrationofdoubleinfinitetodalatticebymeansofinversespectralproblemandrelatedquetions |