Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the distributions of boundary values
of Cauchy integrals


Author: Alexei G. Poltoratski
Journal: Proc. Amer. Math. Soc. 124 (1996), 2455-2463
MSC (1991): Primary 30E20, 30D55; Secondary 42A50
DOI: https://doi.org/10.1090/S0002-9939-96-03363-1
MathSciNet review: 1327037
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We use new methods to give short proofs to some known results on the distributions of boundary values of Cauchy integrals. We also indicate some further generalizations.


References [Enhancements On Off] (What's this?)

  • [A1] A. Aleksandrov, Multiplicity of boundary values of inner functions, Izv. Acad. Nauk. Arm. SSR, Matematica 22 5 (1987), 490--503; English transl., Soviet J. Contemp. Math. Anal. 22 (5) (1987), no. 5, 74--87. MR 89e:30058
  • [A2] A. Aleksandrov, Inner functions and related spaces of pseudocontinuable functions, Proceedings of LOMI seminars 170 (1989), 7--33; English transl., J. Soviet Math. 63 (1993), 115--128. MR 91c:30063
  • [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
  • [C] D. Clark, One dimensional perturbations of restricted shifts, J. Anal. Math. 25 (1972), 169-191. MR 46:692
  • [D1] B. Davis, On the distributions of conjugate functions of nonnegative measures, Duke Math. J. 40 (1973), 695-700. MR 48:2649
  • [D2] B. Davis, On the weak type (1,1) inequality for conjugate functions, Proc. Amer. Math Soc. 44 (1974), 307-311. MR 50:879
  • [Do] W. Donoghue, On the perturbation of spectra, Comm. Pure Appl. Math. 18 (1965), 559-576. MR 32:8171
  • [G] M. Goluzina, On the multiplication and division of Cauchy integrals, Vestnik Leningrad. Univ. Mat. Mekh. Astronom. (1981) no. 4, 8--15; Enlgish transl., Vestnik Leningrad. Univ. Math. 14 (1982), 261--269. MR 84a:30074
  • [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
  • [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
  • [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; English transl., J. Soviet Math. 7 (1977), 317--342. MR 56:12276
  • [T2] O. Tsereteli, Conjugate functions, Mat. Zametki 22 (1977), 771--783; English transl., Math. Notes 22 (1977), 921--928. MR 58:12166
  • [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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30E20, 30D55, 42A50

Retrieve articles in all journals with MSC (1991): 30E20, 30D55, 42A50


Additional Information

Alexei G. Poltoratski
Affiliation: Department of Mathematics 253-37, California Institute of Technology, Pasadena, California 91125
Email: aleksei@cco.caltech.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03363-1
Keywords: Cauchy integral, conjugate functions, singular measures
Received by editor(s): July 27, 1994
Received by editor(s) in revised form: February 24, 1995
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society