Some isometrical identities in the wave equation
We consider the usual wave equation utt(x,t)=c2uxx(x,t) on the real line with some typical initial and boundary conditions. In each case, we establish a natural isometrical identity and inverse formula between the sourse function and the response function.
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171284000132 |
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| _version_ | 1850176532865089536 |
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| author | Saburou Saitoh |
| author_facet | Saburou Saitoh |
| author_sort | Saburou Saitoh |
| collection | DOAJ |
| description | We consider the usual wave equation utt(x,t)=c2uxx(x,t) on the real line with some typical initial and boundary conditions. In each case, we establish a natural isometrical identity and inverse formula between the sourse function and the response function. |
| format | Article |
| id | doaj-art-c22ad5b4eaf042d5b5dbd1fdf4943c26 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c22ad5b4eaf042d5b5dbd1fdf4943c262025-08-20T02:19:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017111713010.1155/S0161171284000132Some isometrical identities in the wave equationSaburou Saitoh0Department of Mathematics, Faculty of Engineering, Gunma University, Kiryu 376, JapanWe consider the usual wave equation utt(x,t)=c2uxx(x,t) on the real line with some typical initial and boundary conditions. In each case, we establish a natural isometrical identity and inverse formula between the sourse function and the response function.http://dx.doi.org/10.1155/S0161171284000132wave equationisometrical identityintegral transformenergy integralinverse transformGreen's functionHilbert space. |
| spellingShingle | Saburou Saitoh Some isometrical identities in the wave equation International Journal of Mathematics and Mathematical Sciences wave equation isometrical identity integral transform energy integral inverse transform Green's function Hilbert space. |
| title | Some isometrical identities in the wave equation |
| title_full | Some isometrical identities in the wave equation |
| title_fullStr | Some isometrical identities in the wave equation |
| title_full_unstemmed | Some isometrical identities in the wave equation |
| title_short | Some isometrical identities in the wave equation |
| title_sort | some isometrical identities in the wave equation |
| topic | wave equation isometrical identity integral transform energy integral inverse transform Green's function Hilbert space. |
| url | http://dx.doi.org/10.1155/S0161171284000132 |
| work_keys_str_mv | AT saburousaitoh someisometricalidentitiesinthewaveequation |