Timeline for Spectral theorem for self-adjoint differential operator on Hilbert space
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
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| Jan 2, 2016 at 22:20 | answer | added | jorge vargas | timeline score: 1 | |
| S May 29, 2015 at 18:52 | history | edited | Manny Reyes | CC BY-SA 3.0 |
Link to WIkipedia page fixed
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| S May 29, 2015 at 18:52 | history | suggested | wdacda | CC BY-SA 3.0 |
Link to WIkipedia page fixed
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| May 29, 2015 at 18:21 | review | Suggested edits | |||
| S May 29, 2015 at 18:52 | |||||
| May 27, 2015 at 19:32 | answer | added | B K | timeline score: 0 | |
| May 27, 2015 at 0:36 | answer | added | wdacda | timeline score: 3 | |
| Oct 11, 2014 at 12:00 | history | edited | Wolfgang |
added sturm-liouville-theory tag
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| Apr 7, 2013 at 4:32 | answer | added | Jonathan Gleason | timeline score: 7 | |
| Mar 27, 2013 at 0:56 | comment | added | Gateau au fromage | You are perfectly right but I am thinking in physical term when you have an observable (self-adjoint linear diff. operator) whose "eigenvectors" generate the whole physical space (i.e. $L^2$). The eigenvectors corresponding to the continuous spectrum are unphysical but they can be added continuously in the form of an integral. In your example, there is only continuous spectrum but the Fourier series is a continuous sum over the unphysical solutions of the eigenvalue problem. | |
| Mar 27, 2013 at 0:45 | vote | accept | Gateau au fromage | ||
| S Mar 27, 2013 at 0:44 | vote | accept | Gateau au fromage | ||
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| Mar 27, 2013 at 0:44 | vote | accept | Gateau au fromage | ||
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| Mar 26, 2013 at 23:44 | vote | accept | Gateau au fromage | ||
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| S Mar 26, 2013 at 23:42 | vote | accept | Gateau au fromage | ||
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| S Mar 26, 2013 at 23:42 | vote | accept | Gateau au fromage | ||
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| Mar 26, 2013 at 23:41 | vote | accept | Gateau au fromage | ||
| S Mar 26, 2013 at 23:42 | |||||
| Mar 26, 2013 at 23:41 | vote | accept | Gateau au fromage | ||
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| Mar 26, 2013 at 21:37 | answer | added | user26107 | timeline score: 5 | |
| Mar 26, 2013 at 20:21 | comment | added | Aaron Hoffman | To be concrete let's take $\partial_x^2$ defined on $H^2(\mathbb{R}) \subset L^2(\mathbb{R})$. What do you mean by eigenvectors? The solutions to the eigenvector equation $u_{xx} = \lambda u$ don't live in $L^2$. If we think of an orthonormal system of eigenvectors as forming the columns of an orthogonal matrix which diagonalizes the operator, perhaps the appropriate generalization is to seek a unitary transformation (Fourier Transform) which conjugates the operator with multiplication (by $-k^2$). | |
| Mar 26, 2013 at 20:18 | answer | added | Igor Khavkine | timeline score: 11 | |
| Mar 26, 2013 at 20:16 | comment | added | András Bátkai | Weidmann's book is an excellent reference on the questions you mention. books.google.hu/books/about/… | |
| Mar 26, 2013 at 19:55 | history | asked | Gateau au fromage | CC BY-SA 3.0 |