|
On the distributions of boundary values of Cauchy integrals
Author(s):
Alexei
G.
Poltoratski
Journal:
Proc. Amer. Math. Soc.
124
(1996),
2455-2463.
MSC (1991):
Primary 30E20, 30D55;
Secondary 42A50
Retrieve article in:
PDF
This article is available free of charge
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:
- [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:
10.1090/S0002-9939-96-03363-1
PII:
S 0002-9939(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
Copyright of article:
Copyright
1996,
American Mathematical Society
|