On the distributions of boundary values of Cauchy integrals

Proceedings of the American Mathematical Society

Volumn 124, Issue 8, 1996, Pages 2455-2463

  Poltoratski, Alexei G ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Cauchy integral; Conjugate functions; Singular measures

Indexed keywords

EID: 21344465808     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-96-03363-1     Document Type: Article

References (18)

1. [A1] A. Aleksandrov, Multiplicity of boundary values of inner functions, Izv. Acad. Nauk. Arm. SSR, Matematica 22 5 (1987), 490-503;
2. English transl., Soviet J. Contemp. Math. Anal. 22 (5) (1987), no. 5, 74-87. MR 89e:30058
3. [A2] A. Aleksandrov, Inner functions and related spaces of pseudocontinuable functions, Proceedings of LOMI seminars 170 (1989), 7-33;
4. English transl., J. Soviet Math. 63 (1993), 115-128. MR 91c:30063
5. [Ar] N. Aronszajn, On a problem of Weyl in the theory of singular Sturm- Liouville equations, Amer. J. Math. 79 (1957), 597-610. MR 19:550
6. [C] D. Clark, One dimensional perturbations of restricted shifts, J. Anal. Math. 25 (1972), 169-191. MR 46:692
7. [D1] B. Davis, On the distributions of conjugate functions of nonnegative measures, Duke Math. J. 40 (1973), 695-700. MR 48:2649
8. [D2] B. Davis, On the weak type (1,1) inequality for conjugate functions, Proc. Amer. Math Soc. 44 (1974), 307-311. MR 50:879
9. [Do] W. Donoghue, On the perturbation of spectra, Comm. Pure Appl. Math. 18 (1965), 559-576. MR 32:8171
10. [G] M. Goluzina, On the multiplication and division of Cauchy integrals, Vestnik Leningrad. Univ. Mat. Mekh. Astronom. (1981) no. 4, 8-15;
11. Enlgish transl., Vestnik Leningrad. Univ. Math. 14 (1982), 261-269. MR 84a:30074
12. [S] B. Simon, Spectral analysis of rank one perturbations and applications, Mathematical Quantum Theory. II: Schrödinger Operators (Vancouver, 1993; J. Feldman et al., editors), CRM Proc. Lecture Notes, vol. 8, Amer. Math. Soc., Providence, RI, 1995, pp. (109-149). CMP 95:12
13. [S-W] B. Simon and T. Wolff, Singular continuous spectrum under rank one perturbations and localisation for random Hamiltonians, Comm. Pure Appl. Math. 39 (1986), 75-90. MR 87k:47032
14. [T1] O. Tsereteli, Metric properties of conjugate functions, Chapter I in B. V. Khvedelidze, Method of Cauchy-type integrals in discontinuous boundary value problems of the theory of holomorphic functions of a complex variable, Itogi Nauki: Sovremennye Problemy Mat., vol. 7, VINITI, Moscow, 1975, pp. 18-57;
15. English transl., J. Soviet Math. 7 (1977), 317-342. MR 56:12276
16. [T2] O. Tsereteli, Conjugate functions, Mat. Zametki 22 (1977), 771-783;
17. English transl., Math. Notes 22 (1977), 921-928. MR 58:12166
18. [V-H] S. Vinogradov and S. Hruschev, Free interpolation in the space of uniformly converging Taylor series, Lecture Notes in Math., vol. 864, Springer-Verlag, Berlin, 1981, pp. (171-213). MR 83b:30032