Abstract
Let $\mu$ be a finite positive measure on the real line. For $a>0$, denote by $\mathcal{E}_a$ the family of exponential functions $$\mathcal{E}_a=\{e^{ist}| s\in[0,a]\}.$$ The exponential type of $\mu$ is the infimum of all numbers $a$ such that the finite linear combinations of the exponentials from $\mathcal{E}_a$ are dense in $L^2(\mu)$. If the set of such $a$ is empty, the exponential type of $\mu$ is defined as infinity. The well-known type problem asks to find the exponential type of $\mu$ in terms of $\mu$. In this note we present a solution to the type problem and discuss its relations with known results.
-
[Bakan]
A. G. Bakan, "Representation of measures with polynomial denseness in $L_p(\Bbb R,d\mu)$, $0<p<\infty$, and its application to determinate moment problems," Proc. Amer. Math. Soc., vol. 136, iss. 10, pp. 3579-3589, 2008.@article {Bakan, MRKEY = {2415042},
AUTHOR = {Bakan, Andrew G.},
TITLE = {Representation of measures with polynomial denseness in {$L\sb p(\Bbb R,d\mu)$},
{$0
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {136},
YEAR = {2008},
NUMBER = {10},
PAGES = {3579--3589},
ISSN = {0002-9939},
CODEN = {PAMYAR},
MRCLASS = {46E30 (41A60 41A65 44A60 47A57)},
MRNUMBER = {2415042},
MRREVIEWER = {Ilaria Mantellini},
DOI = {10.1090/S0002-9939-08-09418-5},
ZBLNUMBER = {1161.46015},
} -
[Benedicks] M. Benedicks, "The support of functions and distributions with a spectral gap," Math. Scand., vol. 55, iss. 2, pp. 285-309, 1984.
@article {Benedicks, MRKEY = {0787203},
AUTHOR = {Benedicks, Michael},
TITLE = {The support of functions and distributions with a spectral gap},
JOURNAL = {Math. Scand.},
FJOURNAL = {Mathematica Scandinavica},
VOLUME = {55},
YEAR = {1984},
NUMBER = {2},
PAGES = {285--309},
ISSN = {0025-5521},
CODEN = {MTSCAN},
MRCLASS = {42A55 (46F12 47A60)},
MRNUMBER = {0787203},
MRREVIEWER = {L. de Branges},
ZBLNUMBER = {0577.42008},
URL = {http://www.mscand.dk/article.php?id=2750},
} -
[Beurling-Stanford] A. Beurling, On quasianalyticity and general distributions, 1961.
@misc{Beurling-Stanford,
author={Beurling, Arne},
TITLE={On quasianalyticity and general distributions},
YEAR={1961},
NOTE={mimeographed lecture notes, Summer institute, Stanford University},
} -
[BM1] A. Beurling and P. Malliavin, "On Fourier transforms of measures with compact support," Acta Math., vol. 107, pp. 291-309, 1962.
@article {BM1, MRKEY = {0147848},
AUTHOR = {Beurling, Arne and Malliavin, P.},
TITLE = {On {F}ourier transforms of measures with compact support},
JOURNAL = {Acta Math.},
FJOURNAL = {Acta Mathematica},
VOLUME = {107},
YEAR = {1962},
PAGES = {291--309},
ISSN = {0001-5962},
MRCLASS = {42.25},
MRNUMBER = {0147848},
MRREVIEWER = {G. Maltese},
DOI = {10.1007/BF02545792},
ZBLNUMBER = {0127.32601},
} -
[BM2] A. Beurling and P. Malliavin, "On the closure of characters and the zeros of entire functions," Acta Math., vol. 118, pp. 79-93, 1967.
@article {BM2, MRKEY = {0209758},
AUTHOR = {Beurling, Arne and Malliavin, Paul},
TITLE = {On the closure of characters and the zeros of entire functions},
JOURNAL = {Acta Math.},
FJOURNAL = {Acta Mathematica},
VOLUME = {118},
YEAR = {1967},
PAGES = {79--93},
ISSN = {0001-5962},
MRCLASS = {42.18 (30.00)},
MRNUMBER = {0209758},
MRREVIEWER = {A. Edrei},
DOI = {10.1007/BF02392477},
ZBLNUMBER = {0171.11901},
} -
[BS] A. Borichev and M. Sodin, "Weighted exponential approximation and non-classical orthogonal spectral measures," Adv. Math., vol. 226, iss. 3, pp. 2503-2545, 2011.
@article{BS, MRKEY={2739783},
AUTHOR = {Borichev, Alexander and Sodin, Mikhail},
TITLE = {Weighted exponential approximation and non-classical orthogonal spectral measures},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {226},
YEAR = {2011},
NUMBER = {3},
PAGES = {2503--2545},
ISSN = {0001-8708},
CODEN = {ADMTA4},
MRCLASS = {34B24 (34B20 41A30 42C10 47E05)},
MRNUMBER = {2739783},
MRREVIEWER = {Mikl{ó}s Horv{á}th},
ZBLNUMBER = {1229.41018},
DOI = {10.1016/j.aim.2010.08.019},
URL = {http://dx.doi.org/10.1016/j.aim.2010.08.019},
} -
[dBr] L. de Branges, Hilbert Spaces of Entire Functions, Englewood Cliffs, NJ: Prentice-Hall, 1968.
@book {dBr, MRKEY = {0229011},
AUTHOR = {de Branges, Louis},
TITLE = {Hilbert Spaces of Entire Functions},
PUBLISHER = {Prentice-Hall},
ADDRESS = {Englewood Cliffs, NJ},
YEAR = {1968},
PAGES = {ix+326},
MRCLASS = {46.30 (30.00)},
MRNUMBER = {0229011},
MRREVIEWER = {J. Rovnyak},
ZBLNUMBER = {0177.16701},
ZBLNUMBER = {0157.43301},
} -
[dBr2] L. de Branges, "Some Hilbert spaces of entire functions. II," Trans. Amer. Math. Soc., vol. 99, pp. 118-152, 1961.
@article {dBr2, MRKEY = {0133456},
AUTHOR = {de Branges, Louis},
TITLE = {Some {H}ilbert spaces of entire functions. {II}},
JOURNAL = {Trans. Amer. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical Society},
VOLUME = {99},
YEAR = {1961},
PAGES = {118--152},
ISSN = {0002-9947},
MRCLASS = {30.85},
MRNUMBER = {0133456},
DOI = {10.2307/1993448},
ZBLNUMBER = {0100.06901},
} -
[DS] R. J. Duffin and A. C. Schaeffer, "Power series with bounded coefficients," Amer. J. Math., vol. 67, pp. 141-154, 1945.
@article {DS, MRKEY = {0011322},
AUTHOR = {Duffin, R. J. and Schaeffer, A. C.},
TITLE = {Power series with bounded coefficients},
JOURNAL = {Amer. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {67},
YEAR = {1945},
PAGES = {141--154},
ISSN = {0002-9327},
MRCLASS = {30.0X},
MRNUMBER = {0011322},
MRREVIEWER = {R. P. Boas, Jr.},
DOI = {10.2307/2371922},
ZBLNUMBER = {0060.20903},
} -
[Dym] H. Dym, "On the span of trigonometric sums in weighted $L^2$ spaces. Problem 12.4," in Linear and Complex Analysis Problem Book 3, Part II, Havin, V. P. and Nikolski, N. K., Eds., New York: Springer-Verlag, 1994, vol. 1574, pp. 87-88.
@incollection{Dym,
author={Dym, H.},
TITLE={On the span of trigonometric sums in weighted {$L^2$} spaces. {P}roblem 12.4},
BOOKTITLE={Linear and Complex Analysis Problem Book 3, Part II},
SERIES={Lecture Notes in Math.},
EDITOR={Havin, V. P. and Nikolski, N. K.},
PUBLISHER={Springer-Verlag},
ADDRESS={New York},
YEAR={1994},
PAGES={87--88},
VOLUME = {1574},
MRNUMBER = {1334346},
ZBLNUMBER = {0893.30037},
DOI = {10.1007/BFb0101060},
} -
[DM] H. Dym and H. P. McKean, Gaussian Processes, Function Theory, and the Inverse Spectral Problem, New York: Academic Press [Harcourt Brace Jovanovich Publishers], 1976, vol. 31.
@book {DM, MRKEY = {0448523},
AUTHOR = {Dym, H. and McKean, H. P.},
TITLE = {Gaussian Processes, Function Theory, and the Inverse Spectral Problem},
SERIES = {Probab. Math. Stat.},
VOLUME={31},
PUBLISHER = {Academic Press [Harcourt Brace Jovanovich Publishers]},
ADDRESS = {New York},
YEAR = {1976},
PAGES = {xi+335},
MRCLASS = {60G25 (30A78 42A08)},
MRNUMBER = {0448523},
MRREVIEWER = {Shinichi Kotani},
ZBLNUMBER = {0327.60029},
} -
[GL] I. M. Gelcprimefand and B. M. Levitan, "On the determination of a differential equation from its spectral function," Izvestiya Akad. Nauk SSSR. Ser. Mat., vol. 15, pp. 309-360, 1951.
@article {GL, MRKEY = {0073805},
AUTHOR = {Gel{\cprime}fand, I. M. and Levitan, B. M.},
TITLE = {On the determination of a differential equation from its spectral function},
JOURNAL = {Izvestiya Akad. Nauk SSSR. Ser. Mat.},
FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
NOTE={English translation in \emph{Amer. Math. Soc. Transl. Ser.} {\bf 2} (1955), 253--304},
VOLUME = {15},
YEAR = {1951},
PAGES = {309--360},
ISSN = {0373-2436},
MRCLASS = {36.0X},
MRNUMBER = {0073805},
MRREVIEWER = {N. Levinson},
ZBLNUMBER = {0066.33603},
} -
[HJ] V. Havin and B. Jöricke, The Uncertainty Principle in Harmonic Analysis, New York: Springer-Verlag, 1994, vol. 28.
@book {HJ, MRKEY = {1303780},
AUTHOR = {Havin, Victor and J{ö}ricke, Burglind},
TITLE = {The Uncertainty Principle in Harmonic Analysis},
SERIES = {Ergeb. Math. Grenzgeb.},
VOLUME = {28},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1994},
PAGES = {xii+543},
ISBN = {3-540-56991-X},
MRCLASS = {42-02 (31B35 42A16 43A45)},
MRNUMBER = {1303780},
MRREVIEWER = {Vladimir Logvinenko},
ZBLNUMBER = {0827.42001},
DOI = {10.1007/978-3-642-78377-7},
} -
[Kerov] S. V. Kerov, "Equilibrium and orthogonal polynomials," Algebra i Analiz, vol. 12, iss. 6, pp. 224-237, 2000.
@article {Kerov, MRKEY = {1816518},
AUTHOR = {Kerov, S. V.},
TITLE = {Equilibrium and orthogonal polynomials},
JOURNAL = {Algebra i Analiz},
FJOURNAL = {Rossiĭskaya Akademiya Nauk. Algebra i Analiz},
VOLUME = {12},
YEAR = {2000},
NUMBER = {6},
PAGES = {224--237},
ISSN = {0234-0852},
MRCLASS = {33C45 (31A15)},
MRNUMBER = {1816518},
MRREVIEWER = {V. Totik},
ZBLNUMBER = {0992.33007},
} -
[KoosisLog] P. Koosis, The Logarithmic Integral. I, Cambridge: Cambridge Univ. Press, 1988, vol. 12.
@book {KoosisLog, MRKEY = {0961844},
AUTHOR = {Koosis, Paul},
TITLE = {The Logarithmic Integral. {I}},
SERIES = {Cambridge Stud. Adv. Math.},
VOLUME = {12},
PUBLISHER = {Cambridge Univ. Press},
ADDRESS = {Cambridge},
YEAR = {1988},
PAGES = {xvi+606},
ISBN = {0-521-30906-9},
MRCLASS = {30D60 (30-02 30E20)},
MRNUMBER = {0961844},
MRREVIEWER = {Burglind J{ö}ricke},
DOI = {10.1017/CBO9780511566196},
ZBLNUMBER = {0665.30038},
} -
[kos3] P. Koosis, The logarithmic integral. II, Cambridge: Cambridge University Press, 1992, vol. 21.
@book {kos3, MRKEY={1195788},
AUTHOR = {Koosis, Paul},
TITLE = {The logarithmic integral. {II}},
SERIES = {Cambridge Studies in Advanced Mathematics},
VOLUME = {21},
PUBLISHER = {Cambridge University Press},
ADDRESS = {Cambridge},
YEAR = {1992},
PAGES = {xxvi+574},
ISBN = {0-521-30907-7},
MRCLASS = {30D15 (26E10 30D30 31A05 31A20 31C15 42A45)},
MRNUMBER = {1195788},
MRREVIEWER = {W. H. J. Fuchs},
ZBLNUMBER = {0791.30020},
DOI = {10.1017/CBO9780511566202},
} -
[Koosis2] P. Koosis, "A local estimate, involving the least superharmonic majorant, for entire functions of exponential type," Algebra i Analiz, vol. 10, iss. 3, pp. 45-64, 1998.
@article {Koosis2, MRKEY = {1628022},
AUTHOR = {Koosis, Paul},
TITLE = {A local estimate, involving the least superharmonic majorant, for entire functions of exponential type},
JOURNAL = {Algebra i Analiz},
FJOURNAL = {Rossiĭskaya Akademiya Nauk. Algebra i Analiz},
VOLUME = {10},
YEAR = {1998},
NUMBER = {3},
PAGES = {45--64},
ISSN = {0234-0852},
MRCLASS = {30D15},
MRNUMBER = {1628022},
ZBLNUMBER = {0920.30020},
} -
[Krein1] M. Krein, "On a problem of extrapolation of A. N. Kolmogoroff," Doklady Akad. Nauk SSSR, vol. 46, pp. 306-309, 1945.
@article {Krein1, MRKEY = {0012700},
AUTHOR = {Krein, M.},
TITLE = {On a problem of extrapolation of {A}. {N}. {K}olmogoroff},
JOURNAL = {Doklady Akad. Nauk SSSR},
VOLUME = {46},
YEAR = {1945},
PAGES = {306--309},
MRCLASS = {42.4X},
MRNUMBER = {0012700},
MRREVIEWER = {S. Bochner},
ZBLNUMBER = {0063.03356},
} -
[Krein2] M. G. Kreuin, "On a basic approximation problem of the theory of extrapolation and filtration of stationary random processes," Doklady Akad. Nauk SSSR, vol. 94, pp. 13-16, 1954.
@article {Krein2, MRKEY = {0062980},
AUTHOR = {Kre{ĭ}n, M. G.},
TITLE = {On a basic approximation problem of the theory of extrapolation and filtration of stationary random processes},
JOURNAL = {Doklady Akad. Nauk SSSR},
VOLUME = {94},
YEAR = {1954},
PAGES = {13--16},
MRCLASS = {60.0X},
MRNUMBER = {0062980},
MRREVIEWER = {N. Levinson},
ZBLNUMBER = {0057.35002},
} -
[Krein3] M. G. Kreuin, "On the transfer function of a one-dimensional boundary problem of the second order," Doklady Akad. Nauk SSSR, vol. 88, pp. 405-408, 1953.
@article {Krein3, MRKEY = {0058072},
AUTHOR = {Kre{ĭ}n, M. G.},
TITLE = {On the transfer function of a one-dimensional boundary problem of the second order},
JOURNAL = {Doklady Akad. Nauk SSSR},
VOLUME = {88},
YEAR = {1953},
PAGES = {405--408},
MRCLASS = {36.0X},
MRNUMBER = {0058072},
MRREVIEWER = {E. A. Coddington},
ZBLNUMBER = {0050.08708},
} -
[LevinBook] Y. B. Levin, Lectures on Entire Functions, Providence, RI: Amer. Math. Soc., 1996, vol. 150.
@book {LevinBook, MRKEY = {1400006},
AUTHOR = {Levin, B. Ya.},
TITLE = {Lectures on Entire Functions},
SERIES = {Transl. Math. Monogr.},
VOLUME = {150},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1996},
PAGES = {xvi+248},
ISBN = {0-8218-0282-8},
MRCLASS = {30-02 (30D15 30D20 31-02 46E99 46J15)},
MRNUMBER = {1400006},
MRREVIEWER = {Vladimir S. Azarin},
ZBLNUMBER = {0856.30001},
} -
[Levin2] Y. B. Levin, "Completeness of systems of functions, quasi-analyticity and subharmonic majorants," Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. $($LOMI$)$, vol. 170, iss. Issled. Linein. Oper. Teorii Funktsii. 17, pp. 102-156, 322, 1989.
@article {Levin2, MRKEY = {1039577},
AUTHOR = {Levin, B. Ya.},
TITLE = {Completeness of systems of functions, quasi-analyticity and subharmonic majorants},
JOURNAL = {Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. $($LOMI$)$},
FJOURNAL = {Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta imeni V. A. Steklova Akademii Nauk SSSR (LOMI)},
VOLUME = {170},
YEAR = {1989},
NUMBER = {Issled. Linein. Oper. Teorii Funktsii. 17},
PAGES = {102--156, 322--323},
ISSN = {0373-2703},
MRCLASS = {46E99 (30D60 31A99)},
MRNUMBER = {1039577},
MRREVIEWER = {Plamen Dzhakov},
DOI = {10.1007/BF01099310},
ZBLNUMBER = {0701.30006},
} -
[Levinson] N. Levinson, Gap and Density Theorems, New York: Amer. Math. Soc., 1940, vol. 26.
@book {Levinson, MRKEY = {0003208},
AUTHOR = {Levinson, Norman},
TITLE = {Gap and {D}ensity {T}heorems},
SERIES = {Amer. Math. Soc. Colloq. Publ.},
VOLUME={26},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {New York},
YEAR = {1940},
PAGES = {viii+246},
MRCLASS = {27.0X},
MRNUMBER = {0003208},
MRREVIEWER = {G. P{ó}lya},
ZBLNUMBER = {0145.08003},
} -
[MIF1] N. Makarov and A. Poltoratski, "Meromorphic inner functions, Toeplitz kernels and the uncertainty principle," in Perspectives in Analysis, New York: Springer-Verlag, 2005, vol. 27, pp. 185-252.
@incollection {MIF1, MRKEY = {2215727},
AUTHOR = {Makarov, N. and Poltoratski, A.},
TITLE = {Meromorphic inner functions, {T}oeplitz kernels and the uncertainty principle},
BOOKTITLE = {Perspectives in Analysis},
SERIES = {Math. Phys. Stud.},
VOLUME = {27},
PAGES = {185--252},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {2005},
MRCLASS = {47B35 (30C40 46E22 47B32 47E05)},
MRNUMBER = {2215727},
MRREVIEWER = {Anton Baranov},
DOI = {10.1007/3-540-30434-7_10},
ZBLNUMBER = {1118.47020},
} -
[MIF2] N. Makarov and A. Poltoratski, "Beurling-Malliavin theory for Toeplitz kernels," Invent. Math., vol. 180, iss. 3, pp. 443-480, 2010.
@article {MIF2, MRKEY = {2609247},
AUTHOR = {Makarov, N. and Poltoratski, A.},
TITLE = {Beurling-{M}alliavin theory for {T}oeplitz kernels},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {180},
YEAR = {2010},
NUMBER = {3},
PAGES = {443--480},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {47B35 (30J10 42B10 46E22)},
MRNUMBER = {2609247},
MRREVIEWER = {Kristian Seip},
DOI = {10.1007/s00222-010-0234-2},
ZBLNUMBER = {1186.47025},
} -
[Polya] M. Mitkovski and A. Poltoratski, "Pólya sequences, Toeplitz kernels and gap theorems," Adv. Math., vol. 224, iss. 3, pp. 1057-1070, 2010.
@article {Polya, MRKEY = {2628803},
AUTHOR = {Mitkovski, Mishko and Poltoratski, Alexei},
TITLE = {Pólya sequences, {T}oeplitz kernels and gap theorems},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {224},
YEAR = {2010},
NUMBER = {3},
PAGES = {1057--1070},
ISSN = {0001-8708},
CODEN = {ADMTA4},
MRCLASS = {30D15 (42B10 46E22 47B35)},
MRNUMBER = {2628803},
MRREVIEWER = {A. B{ö}ttcher},
DOI = {10.1016/j.aim.2009.12.014},
ZBLNUMBER = {1204.30018},
} -
[Ni1] N. K. Nikolcprimeskiui, "Bases of exponentials and values of reproducing kernels," Dokl. Akad. Nauk SSSR, vol. 252, iss. 6, pp. 1316-1320, 1980.
@article {Ni1, MRKEY = {0576140},
AUTHOR = {Nikol{\cprime}ski{\u\i},
N. K.},
TITLE = {Bases of exponentials and values of reproducing kernels},
JOURNAL = {Dokl. Akad. Nauk SSSR},
FJOURNAL = {Doklady Akademii Nauk SSSR},
VOLUME = {252},
YEAR = {1980},
NUMBER = {6},
PAGES = {1316--1320},
ISSN = {0002-3264},
MRCLASS = {30B60 (30C40 30D50)},
MRNUMBER = {0576140},
MRREVIEWER = {M. {Ī}. Nagnib{\=ı}da},
} -
[Ni2] N. K. Nikolcprimeskiui, Treatise on the Shift Operator, New York: Springer-Verlag, 1986, vol. 273.
@book {Ni2, MRKEY = {0827223},
AUTHOR = {Nikol{\cprime}ski{\u\i},
N. K.},
TITLE = {Treatise on the Shift Operator},
SERIES = {Grundl. Math. Wissen.},
VOLUME = {273},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1986},
PAGES = {xii+491},
ISBN = {3-540-15021-8},
MRCLASS = {47B37 (30H05 47-02 47B35)},
MRNUMBER = {0827223},
MRREVIEWER = {J. Rovnyak},
DOI = {10.1007/978-3-642-70151-1},
ZBLNUMBER = {0587.47036},
} -
[Clark] A. Poltoratski, "Boundary behavior of pseudocontinuable functions," Algebra i Analiz, vol. 5, iss. 2, pp. 189-210, 1993.
@article {Clark, MRKEY = {1223178},
AUTHOR = {Poltoratski, Alexei},
TITLE = {Boundary behavior of pseudocontinuable functions},
JOURNAL = {Algebra i Analiz},
FJOURNAL = {Rossiĭskaya Akademiya Nauk. Algebra i Analiz},
VOLUME = {5},
YEAR = {1993},
NUMBER = {2},
PAGES = {189--210},
ISSN = {0234-0852},
MRCLASS = {30D55},
MRNUMBER = {1223178},
MRREVIEWER = {D. Sarason},
ZBLNUMBER = {0833.30018},
} -
[GAP] A. Poltoratski, "Spectral gaps for sets and measures," Acta Math., vol. 208, iss. 1, pp. 151-209, 2012.
@article {GAP, MRKEY = {2910798},
AUTHOR = {Poltoratski, Alexei},
TITLE = {Spectral gaps for sets and measures},
JOURNAL = {Acta Math.},
FJOURNAL = {Acta Mathematica},
VOLUME = {208},
YEAR = {2012},
NUMBER = {1},
PAGES = {151--209},
ISSN = {0001-5962},
CODEN = {ACMAA8},
MRCLASS = {42A38 (28A12 30D15 43A10 47B35)},
MRNUMBER = {2910798},
MRREVIEWER = {George A. Willis},
DOI = {10.1007/s11511-012-0076-4},
ZBLNUMBER = {1245.42008},
} -
[PS] A. Poltoratski and D. Sarason, "Aleksandrov-Clark measures," in Recent Advances in Operator-Related Function Theory, Providence, RI: Amer. Math. Soc., 2006, vol. 393, pp. 1-14.
@incollection {PS, MRKEY = {2198367},
AUTHOR = {Poltoratski, Alexei and Sarason, Donald},
TITLE = {Aleksandrov-{C}lark measures},
BOOKTITLE = {Recent Advances in Operator-Related Function Theory},
SERIES = {Contemp. Math.},
VOLUME = {393},
PAGES = {1--14},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {2006},
MRCLASS = {30D50 (30D55 30E05 30E20 47A45 47A55 47B15 47B33)},
MRNUMBER = {2198367},
MRREVIEWER = {Javad Mashreghi},
DOI = {10.1090/conm/393/07366},
ZBLNUMBER = {1102.30032},
}
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