Uloženo v:
| Hlavní autoři: | , , |
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| Médium: | Preprint |
| Vydáno: |
1998
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| Témata: | |
| On-line přístup: | https://arxiv.org/abs/math/9812052 |
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Obsah:
- We consider existence and uniqueness of symmetric approximation of frames by normalized tight frames and of symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces H . More precisely, we determine whether a given frame or basis possesses a normalized tight frame or orthonormal basis that is quadratically closest to it, if there exists such frames or bases at all. A crucial role is played by the Hilbert-Schmidt property of the operator (P-|F|), where F is the adjoint operator of the frame transform F*: H --> l_2 of the initial frame or basis and (1-P) is the projection onto the kernel of F. The result is useful in wavelet theory.