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A convergent approximation scheme for the inverse Sturm-Liouville problem
| Content Provider | Scilit |
|---|---|
| Author | Seidman, T. I. |
| Copyright Year | 1985 |
| Description | Journal: Inverse Problems For the Sturm-Liouville operator $L=L_{p}$:y mod to -y"+py one seeks to reconstruct the coefficient p from knowledge of the sequence of eigen-frequencies ( lambda$ _{j}$ with $Ly_{j}$= lambda$ _{j}y_{j}$ for some $y_{j}$ not=0). An implementable scheme is: for some N determine $p_{N}$ so (approximately) $p_{N}$ has minimum norm with eigen-frequencies ( lambda$ _{1}$,. . ., lambda$ _{N}$) as given. This is the method of 'generalised interpolation' and is shown to give a convergent approximation scheme: $p_{N}$ to p. The principal technical difficulties are the continuities of the functionals p mod to lambda$ _{j}$, which are shown for p topologised by weak convergence in $(H^{1}$)', and the injectivity of p mod to ( lambda$ _{j}$:j=1,2,. . .). |
| Related Links | http://pdfs.semanticscholar.org/8f35/dfa1d1f39353c8f8674164986e0f027375b9.pdf http://iopscience.iop.org/article/10.1088/0266-5611/1/3/009/pdf |
| Ending Page | 262 |
| Page Count | 12 |
| Starting Page | 251 |
| ISSN | 02665611 |
| e-ISSN | 13616420 |
| DOI | 10.1088/0266-5611/1/3/009 |
| Journal | Inverse Problems |
| Issue Number | 3 |
| Volume Number | 1 |
| Language | English |
| Publisher | IOP Publishing |
| Publisher Date | 1985-08-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Inverse Problems Applied Mathematics Weak Convergence Sturm Liouville Problem |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Theoretical Computer Science Signal Processing Mathematical Physics Computer Science Applications |
