{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T21:20:34Z","timestamp":1742937634783,"version":"3.40.3"},"publisher-location":"Cham","reference-count":15,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319684444"},{"type":"electronic","value":"9783319684451"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-68445-1_46","type":"book-chapter","created":{"date-parts":[[2017,10,23]],"date-time":"2017-10-23T20:40:36Z","timestamp":1508791236000},"page":"393-398","source":"Crossref","is-referenced-by-count":1,"title":["Quantum Harmonic Analysis and the Positivity of Trace Class Operators; Applications to\u00a0Quantum Mechanics"],"prefix":"10.1007","author":[{"given":"Elena","family":"Nicola","sequence":"first","affiliation":[]},{"given":"Maurice","family":"de Gosson","sequence":"additional","affiliation":[]},{"given":"Fabio","family":"Nicola","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,10,24]]},"reference":[{"key":"46_CR1","doi-asserted-by":"crossref","DOI":"10.1515\/9781400881994","volume-title":"Lectures on Fourier Integrals","author":"S Bochner","year":"1959","unstructured":"Bochner, S.: Lectures on Fourier Integrals. Princeton University Press, Princeton (1959)"},{"issue":"1","key":"46_CR2","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1063\/1.531326","volume":"36","author":"T Br\u00f6cker","year":"1995","unstructured":"Br\u00f6cker, T., Werner, R.F.: Mixed states with positive Wigner functions. J. Math. Phys. 36(1), 62\u201375 (1995)","journal-title":"J. Math. Phys."},{"key":"46_CR3","unstructured":"Cordero, E., de Gosson, M., Nicola, F.: On the positivity of trace-class operators, Submitted. ArXiv:1706.06171"},{"issue":"1","key":"46_CR4","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/S0034-4877(09)00008-1","volume":"63","author":"NC Dias","year":"2009","unstructured":"Dias, N.C., Prata, J.N.: The Narcowich-Wigner spectrum of a pure state. Rep. Math. Phys. 63(1), 43\u201354 (2009)","journal-title":"Rep. Math. Phys."},{"key":"46_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7643-9992-4","volume-title":"Symplectic Methods in Harmonic Analysis and in Mathematical Physics","author":"M Gosson de","year":"2011","unstructured":"de Gosson, M.: Symplectic Methods in Harmonic Analysis and in Mathematical Physics. Birkh\u00e4user, Basel (2011)"},{"key":"46_CR6","unstructured":"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0375960117307004"},{"key":"46_CR7","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/BF01649588","volume":"1","author":"D Kastler","year":"1965","unstructured":"Kastler, D.: The $$C^{\\ast }$$ -Algebras of a free boson field. Commun. Math. Phys. 1, 14\u201348 (1965)","journal-title":"Commun. Math. Phys."},{"key":"46_CR8","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/BF01773339","volume":"2","author":"G Loupias","year":"1966","unstructured":"Loupias, G., Miracle-Sole, S.: $$C^{\\ast }$$ -Alg\u00e8bres des syst\u00e8mes canoniques, I. Commun. Math. Phys. 2, 31\u201348 (1966)","journal-title":"Commun. Math. Phys."},{"issue":"1","key":"46_CR9","first-page":"39","volume":"6","author":"G Loupias","year":"1967","unstructured":"Loupias, G., Miracle-Sole, S.: $$C^{\\ast }$$ -Alg\u00e8bres des syst\u00e8mes canoniques, II. Ann. Inst. Henri Poincar\u00e9 6(1), 39\u201358 (1967)","journal-title":"Ann. Inst. Henri Poincar\u00e9"},{"key":"46_CR10","doi-asserted-by":"crossref","first-page":"1208","DOI":"10.1046\/j.1365-8711.2001.04840.x","volume":"327","author":"MT Murphy","year":"2001","unstructured":"Murphy, M.T., Webb, J.K., Flambaum, V.V., Dzuba, V.A., Churchill, C.W., Prochaska, J.X., Barrow, J.D., Wolfe, A.M.: Possible evidence for a variable fine-structure constant from QSO absorption lines: motivations, analysis and results. Mon. Not. R. Astron. Soc. 327, 1208\u20131222 (2001)","journal-title":"Mon. Not. R. Astron. Soc."},{"issue":"2","key":"46_CR11","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1046\/j.1365-8711.2003.06970.x","volume":"345","author":"MT Murphy","year":"2003","unstructured":"Murphy, M.T., Webb, J.K., Flambaum, V.V.: Further evidence for a variable fine-structure constant from Keck\/HIRES QSO absorption spectra. Mon. Not. R. Astron. Soc. 345(2), 609\u2013638 (2003)","journal-title":"Mon. Not. R. Astron. Soc."},{"issue":"9","key":"46_CR12","doi-asserted-by":"crossref","first-page":"2036","DOI":"10.1063\/1.527861","volume":"29","author":"FJ Narcowich","year":"1988","unstructured":"Narcowich, F.J.: Conditions for the convolution of two Wigner distributions to be itself a Wigner distribution. J. Math. Phys. 29(9), 2036\u20132041 (1988)","journal-title":"J. Math. Phys."},{"issue":"11","key":"46_CR13","doi-asserted-by":"crossref","first-page":"2565","DOI":"10.1063\/1.528537","volume":"30","author":"FJ Narcowich","year":"1989","unstructured":"Narcowich, F.J.: Distributions of $$\\eta $$ -positive type and applications. J. Math. Phys. 30(11), 2565\u20132573 (1989)","journal-title":"J. Math. Phys."},{"issue":"2","key":"46_CR14","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1063\/1.528922","volume":"31","author":"FJ Narcowich","year":"1990","unstructured":"Narcowich, F.J.: Geometry and uncertainty. J. Math. Phys. 31(2), 354\u2013364 (1990)","journal-title":"J. Math. Phys."},{"issue":"1","key":"46_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/PhysRevA.34.1","volume":"34","author":"FJ Narcowich","year":"1986","unstructured":"Narcowich, F.J., O\u2019Connell, R.F.: Necessary and sufficient conditions for a phase-space function to be a Wigner distribution. Phys. Rev. A 34(1), 1\u20136 (1986)","journal-title":"Phys. Rev. A"}],"container-title":["Lecture Notes in Computer Science","Geometric Science of Information"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-68445-1_46","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,4]],"date-time":"2019-10-04T21:58:20Z","timestamp":1570226300000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-68445-1_46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319684444","9783319684451"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-68445-1_46","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}