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Zur Theorie der linearen und nichtlinearen Integralgleichungen: I. Teil: Entwicklung willk�rlicher Funktionen nach Systemen vorgeschriebener
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Coleman, A. J. (1963) · Reviews of Modern Physics · doi:10.1103/revmodphys.35.668 · Cited by 1,506
Entanglement measures and purification procedures
Vedral, V., & Plenio, M. B. (1998) · Physical Review A · doi:10.1103/physreva.57.1619 · Cited by 1,419
Entanglement spectrum of a topological phase in one dimension
Pollmann, F., Turner, A. M., Berg, E., & Oshikawa, M. (2010) · Physical Review B · doi:10.1103/physrevb.81.064439 · Cited by 1,341
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Brunton, S. L., & Kutz, J. N. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108380690 · Cited by 1,154
Schumacher, B. (1995) · Physical Review A · doi:10.1103/physreva.51.2738 · Cited by 1,090
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Stewart, G. W. (1993) · SIAM Review · doi:10.1137/1035134 · Cited by 985
Karhunen–Loève procedure for gappy data
Everson, R., & Sirovich, L. (1995) · Journal of the Optical Society of America A · doi:10.1364/josaa.12.001657 · Cited by 906
A complete classification of quantum ensembles having a given density matrix
Hughston, L. P., Jozsa, R., & Wootters, W. K. (1993) · Physics Letters A · doi:10.1016/0375-9601(93)90880-9 · Cited by 649
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Vidal, G., & Tarrach, R. (1999) · Physical Review A · doi:10.1103/physreva.59.141 · Cited by 599
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Zeh, H. D. (1973) · Foundations of Physics · doi:10.1007/bf00708603 · Cited by 134
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Metadata
- Authors
- Schmidt, E.
- Venue
- Mathematische Annalen
- Published
- 1907-12
- Volume
- 63
- Issue
- 4
- Pages
- 433-476
- ISSN
- 0025-5831 (ISSN-L)
- 1432-1807
- OpenAlex
- W2323980249
- Cited by
- 973
- References
- 0
- FWCI
- 33.25
- Type
- journal article
- Language
- de
- Open access
- green
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