Abstract
Necessary and sufficient conditions are presented for a positive measure to be the spectral measure of a halfline Schrödinger operator with square integrable potential.

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VOLUME = {150},
YEAR = {1999},
NUMBER = {3},
PAGES = {10291057},
ISSN = {0003486X},
CODEN = {ANMAAH},
MRCLASS = {34L05 (34A55 34B24 47E05)},
MRNUMBER = {2001m:34185a},
MRREVIEWER = {Paul E. Sacks},
ZBLNUMBER = {0945.34013},
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[Sim288] B. Simon, "A canonical factorization for meromorphic Herglotz functions on the unit disk and sum rules for Jacobi matrices," J. Funct. Anal., vol. 214, iss. 2, pp. 396409, 2004.
@article {Sim288, MRKEY = {2083307},
AUTHOR = {Simon, Barry},
TITLE = {A canonical factorization for meromorphic {H}erglotz functions on the unit disk and sum rules for {J}acobi matrices},
JOURNAL = {J. Funct. Anal.},
FJOURNAL = {Journal of Functional Analysis},
VOLUME = {214},
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NUMBER = {2},
PAGES = {396409},
ISSN = {00221236},
CODEN = {JFUAAW},
MRCLASS = {47B36 (30D30 30D50 39A70)},
MRNUMBER = {2005j:47033},
MRREVIEWER = {Jan Janas},
DOI = {10.1016/j.jfa.2003.11.006},
ZBLNUMBER = {1064.30030},
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AUTHOR = {Simon, Barry},
TITLE = {Orthogonal Polynomials on the Unit Circle. {P}art 1, Classical Theory},
SERIES = {Amer. Math. Soc. Colloq. Publ.},
NUMBER = {54},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {2005},
PAGES = {xxvi+466},
ISBN = {0821834460},
MRCLASS = {4202 (30C85 33C45 42C05 47B36 47N50)},
MRNUMBER = {2006a:42002a},
MRREVIEWER = {P. L. Duren},
ZBLNUMBER = {1082.42020},
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[OPUC2] B. Simon, Orthogonal Polynomials on the Unit Circle. Part 2, Spectral Theory, Providence, RI: Amer. Math. Soc., 2005.
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AUTHOR = {Simon, Barry},
TITLE = {Orthogonal Polynomials on the Unit Circle. {P}art 2, Spectral Theory},
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MRNUMBER = {2006a:42002b},
MRREVIEWER = {P. L. Duren},
ZBLNUMBER = {1082.42021},
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AUTHOR = {Simon, Barry and Zlato{š},
Andrej},
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VOLUME = {242},
YEAR = {2003},
NUMBER = {3},
PAGES = {393423},
ISSN = {00103616},
CODEN = {CMPHAY},
MRCLASS = {42C05 (15A18 39A70 47B36)},
MRNUMBER = {2005f:42057},
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ZBLNUMBER = {1046.42017},
} 
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JOURNAL = {Funktsional. Anal. i Prilozhen.},
FJOURNAL = {Rossiĭskaya Akademiya Nauk. Funktsional' nyĭAnaliz i ego Prilozheniya},
VOLUME = {34},
YEAR = {2000},
NUMBER = {2},
PAGES = {5062, 96},
ISSN = {03741990},
MRCLASS = {34L05 (34A55 47A99 47E05)},
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} 
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@book {Stein, MRKEY = {1232192},
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} 
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} 
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@book{Szb,
author={Szegő, G.},
TITLE={Orthogonal Polynomials},
EDITION={{T}hird},
SERIES= {Amer. Math. Soc. Colloq. Publ.},
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@book {Titchmarsh, MRKEY = {0176151},
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} 
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@article {ZF, MRKEY = {0303132},
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JOURNAL = {Funkcional. Anal. i Priložen.},
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VOLUME = {5},
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PAGES = {1827},
ISSN = {03741990},
MRCLASS = {35Q99 (47F05)},
MRNUMBER = {46 \#2270},
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}