On $A$-integrability of the spectral shift function of unitary operators arising in the Lax-Phillips scattering theory

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On $A$-integrability of the spectral shift function of unitary operators arising in the Lax-Phillips scattering theory

A. V. Rybkin

Source: Duke Math. J. Volume 83, Number 3 (1996), 683-699.

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Primary Subjects: 58G25

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077244651
Mathematical Reviews number (MathSciNet): MR1390661
Zentralblatt MATH identifier: 0876.47010
Digital Object Identifier: doi:10.1215/S0012-7094-96-08322-2

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References

[1] V. M. Adamjan and D. Z. Arov, Unitary couplings of semi-unitary operators, Mat. Issled. 1 (1966), no. vyp. 2, 3–64, English translation in Amer. Math. Soc. Transl. Ser. 2 95, 1970.

Mathematical Reviews (MathSciNet): MR34:6528

Zentralblatt MATH: 0258.47012

[2] V. M. Adamjan and H. Neidhardt, On the summability of the spectral shift function for pair of contractions and dissipative operators, J. Operator Theory 24 (1990), no. 1, 187–205.

Mathematical Reviews (MathSciNet): MR92d:47016

Zentralblatt MATH: 0795.47023

[3] A. B. Aleksandrov, $A$-integrability of boundary values of harmonic functions, Mat. Zametki 30 (1981), no. 1, 59–72, 154.

Mathematical Reviews (MathSciNet): MR83j:30039

Zentralblatt MATH: 0471.30032

[4] D. Z. Arov, Unitary couplings with losses (a theory of scattering with losses), Funkcional. Anal. i Priložen. 8 (1974), no. 4, 5–22.

Mathematical Reviews (MathSciNet): MR50:10864

Zentralblatt MATH: 0307.47010

[5] M. Sh. Birman and M. G. Krein, On the theory of wave operators and scattering operators, Dokl. Akad. Nauk SSSR 144 (1962), 475–478, English translation in Soviet Math. Dokl. 3 (1962).

Mathematical Reviews (MathSciNet): MR25:2447

Zentralblatt MATH: 0196.45004

[6] M. Sh. Birman and D. R. Yafaev, The spectral shift function. The papers of M. G. Kreĭn and their further development, Algebra i Analiz 4 (1992), no. 5, 1–44.

Mathematical Reviews (MathSciNet): MR94g:47002

Zentralblatt MATH: 0791.47013

[7] D. Bollé, F. Gesztesy, H. Grosse, and B. Simon, Kreĭn's spectral shift function and Fredholm determinants as efficient methods to study supersymmetric quantum mechanics, Lett. Math. Phys. 13 (1987), no. 2, 127–133.

Mathematical Reviews (MathSciNet): MR88f:81043

Zentralblatt MATH: 0626.46062

Digital Object Identifier: doi:10.1007/BF00955200

[8] N. Borisov, W. Muller, and R. Schrader, Relative index theorems and supersymmetric scattering theory, Comm. Math. Phys. 114 (1988), no. 3, 475–513.

Mathematical Reviews (MathSciNet): MR89j:58131

Zentralblatt MATH: 0663.58032

Digital Object Identifier: doi:10.1007/BF01242140

Project Euclid: euclid.cmp/1104160691

[9] J. B. Garnett, Bounded Analytic Functions, Pure Appl. Math., vol. 96, Academic Press, New York, 1981.

Mathematical Reviews (MathSciNet): MR83g:30037

Zentralblatt MATH: 0469.30024

[10] F. Gesztesy, H. Holden, and B. Simon, Absolute summability of the trace relation for certain Schrodinger operators, Comm. Math. Phys. 168 (1995), no. 1, 137–161.

Mathematical Reviews (MathSciNet): MR96b:34110

Zentralblatt MATH: 0821.34076

Digital Object Identifier: doi:10.1007/BF02099586

Project Euclid: euclid.cmp/1104272288

[11] F. Gesztesy, H. Holden, B. Simon, and Z. Zhao, Trace formulae and inverse spectral theory for Schrodinger operators, Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 2, 250–255.

Mathematical Reviews (MathSciNet): MR94c:34127

Zentralblatt MATH: 0786.34081

Digital Object Identifier: doi:10.1090/S0273-0979-1993-00431-2

[12] F. Gesztesy and B. Simon, Topological invariance of the Witten index, J. Funct. Anal. 79 (1988), no. 1, 91–102.

Mathematical Reviews (MathSciNet): MR90a:47032

Zentralblatt MATH: 0649.47012

Digital Object Identifier: doi:10.1016/0022-1236(88)90031-6

[13] I. Ts. Gohberg and M. G. Krein, Introduction to the Theory of Linear Non-selfadjoint Operators in Hilbert Space, Izdat. “Nauka”, Moscow, 1965, English translation published by Amer. Math. Soc., Providence, 1969.

Mathematical Reviews (MathSciNet): MR220070

[14] L. S. Koplienko, Local conditions for the existence of the function of spectral shift, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 73 (1977), 102–117, 232 (1978), English translation in J. Soviet Math. 34 (1986), 2080–2090.

Mathematical Reviews (MathSciNet): MR80a:47035

Zentralblatt MATH: 0406.47006

[15] L. S. Koplienko, The trace formula for perturbations of nonnuclear type, Sibirsk. Mat. Zh. 25 (1984), no. 5, 62–71.

Mathematical Reviews (MathSciNet): MR86g:47012

Zentralblatt MATH: 0574.47021

[16] M. G. Krein, On perturbation determinants and a trace formula for unitary and self-adjoint operators, Dokl. Akad. Nauk SSSR 144 (1962), 268–271, English translation in Soviet Math Dokl. 3 (1962), 707–710.

Mathematical Reviews (MathSciNet): MR25:2446

Zentralblatt MATH: 0191.15201

[17] M. G. Krein, On the trace formula in perturbation theory, Mat. Sbornik N.S. 33(75) (1953), 597–626.

Mathematical Reviews (MathSciNet): MR15,720b

Zentralblatt MATH: 0052.12303

[18] M. G. Krein, Some new studies in the theory of perturbations of self-adjoint operators, First Math. Summer School, Part I (Russian), Izdat. “Naukova Dumka”, Kiev, 1964, English translation in Topics in Differential and Integral Equations and Operator Theory, Birkhäuser-Verlag, Basel, 1983, pp. 103–187.

Mathematical Reviews (MathSciNet): MR32:2919

[19] P. Lax and R. Phillips, Scattering Theory, 2nd ed., Pure Appl. Math., vol. 26, Academic Press, Boston, 1989.

Mathematical Reviews (MathSciNet): MR90k:35005

Zentralblatt MATH: 0697.35004

[20] I. M. Lifshitz, On a problem of perturbation theory, Uspekhi Mat. Nauk 7 (1952), 171–180 (Russian).

[21] S. N. Naboko, On the boundary values of analytic operator-valued functions with a positive imaginary part, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 157 (1987), no. Issled. po Linein. Operator. i Teorii Funktsii. XVI, 55–69, 179, English translation in J. Soviet Math. 44 (1989) 786–795.

Mathematical Reviews (MathSciNet): MR88m:47022

Zentralblatt MATH: 0643.47013

[22] N. K. Nikol'skii and S. V. Khrushchev, A functional model and some problems of the spectral theory of functions, Proc. Steklov Inst. Math. (1988), 101–214, issue 3.

Zentralblatt MATH: 0665.47007

Mathematical Reviews (MathSciNet): MR902373

[23] B. S. Pavlov, Calculation of losses in scattering problems, Mat. Sb. (N.S.) 97(139) (1975), no. 1(5), 77–93, 159, English translation in Math. USSR Sb. 26 (1975), 71–87.

Mathematical Reviews (MathSciNet): MR52:6465

Zentralblatt MATH: 0325.47007

[24] B. S. Pavlov, Dilation theory and spectral analysis of nonselfadjoint differential operators, Mathematical Programming and Related Questions (Proc. Seventh Winter School, Drogobych, 1974), Theory of operators in linear spaces (Russian), Central. Ekonom. Mat. Inst. Akad. Nauk SSSR, Moscow, 1976, English translation in Amer. Math. Soc. Transl. Ser. 2 115, 1980, pp. 3–69.

Mathematical Reviews (MathSciNet): MR58:30375

Zentralblatt MATH: 0516.47007

[25] B. S. Pavlov, A trace formula for a contractive and a unitary operator, Funktsional. Anal. i Prilozhen. 21 (1987), no. 4, 85–87, English translation in Functional Anal. Appl. 21 (1987), 334–336.

Mathematical Reviews (MathSciNet): MR89e:47014

Zentralblatt MATH: 0643.47023

[26] A. V. Rybkin, Convergence of arguments of Blaschke products in $L_ p$-metrics, Proc. Amer. Math. Soc. 111 (1991), no. 3, 701–708.

Mathematical Reviews (MathSciNet): MR91f:30046

Zentralblatt MATH: 0718.30022

Digital Object Identifier: doi:10.2307/2048407

[27] A. V. Rybkin, The discrete and the singular spectrum in the trace formula for a contractive and a unitary operator, Funktsional. Anal. i Prilozhen. 23 (1989), no. 3, 84–85, English translation in Functional Anal. Appl. 23 (1989), 242–246.

Mathematical Reviews (MathSciNet): MR90k:47010

Zentralblatt MATH: 0705.47004

[28] A. V. Rybkin, The spectral shift function, the characteristic function of a contraction and a generalized integral, Mat. Sb. 185 (1994), no. 10, 91–144, English translation in Russian Acad. Sci. Sb. Math. 83 (1995), 237–281.

Mathematical Reviews (MathSciNet): MR96k:47002

Zentralblatt MATH: 0852.47004

[29] B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators on Hilbert Space, rev. ed., Translated from the French and revised, North-Holland, Amsterdam, 1970.

Mathematical Reviews (MathSciNet): MR43:947

Zentralblatt MATH: 0201.45003

[30] P. L. Ul'yanov, The $A$-integral and conjugate functions, Moskov. Gos. Univ. Uč. Zap. Mat. 181(8) (1956), 139–157.

Mathematical Reviews (MathSciNet): MR18,892d

[31] D. R. Yafaev, Mathematical scattering theory, Translations of Mathematical Monographs, vol. 105, American Mathematical Society, Providence, RI, 1992.

Mathematical Reviews (MathSciNet): MR94f:47012

Zentralblatt MATH: 0761.47001

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