Skip to main content
Log in

On exponential representations of analytic functions in the upper half-plane with positive imaginary part

  • Published:
Journal d’Analyse Mathématique Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Bibliography

  1. Achiezer, N. I. and Krein M. G., On certain problems in the theory of moments, Kharkoff (1938) (Russian).

  2. Aronszajn, N., On a problem of Weyl in the theory of singular Sturm-Liouville equations.Am. Journ. of Math. 79 (1957), pp. 597–610.

    Article  MATH  MathSciNet  Google Scholar 

  3. Aronszajn, N., Rayleigh-Ritz and A. Weinstein methods for approximation of eigenvalues I. Operators in a Hilbert space.Proc. of Nat. Ac. Sci. 34 (1948) pp. 474–480.

    Article  MATH  Google Scholar 

  4. Besicovitch, A. S., On a general metric property of summable functions,Journ. London Math. Soc. vol. 1 (1926), pp. 120–128.

    Article  Google Scholar 

  5. Delange, H., On two theorems of S. Verblunsky.Proc. Camb. Phil. Soc. vol. 46 (1950) pp. 57–66.

    MATH  MathSciNet  Google Scholar 

  6. Doob, J. L., and Koopman, B. O., On analytic functions with positive imaginary parts,Bull. Amer. Math. Soc. vol. 40 (1934) pp. 601–605.

    Article  MathSciNet  Google Scholar 

  7. Evans, G. C., The Logarithmic Potential.Am. Math. Soc. Colloquium Publications vol. VI (1927).

  8. Gelfand, I. M. and Levitan, B. M., On the determination of a differential equation from its spectral function,Izvestia Akad. Nauk USSR Ser. Math. vol. 15 (1951) (Russian).

  9. Katz, I. S., On the integral representation of analytic functions mapping the upper half-plane into itself,Uspehi Math. Nauk vol. 113 (69), (1956), pp. 139–144 (Russian).

    Google Scholar 

  10. Kolmogoroff, A., Sur les fonctions harmoniques conjuguées et les séries de Fourier.Fund. Math. vol. 7 (1925) pp. 24–29.

    MATH  Google Scholar 

  11. Krein, M. G., On a method of effective solution of an inverse boundary problem.Dokl. Akad. Nauk USSR 94 (1954) p. 420 (Russian).

    Google Scholar 

  12. Kryloff, W., Ueber Funktionen die in der Halbebene regulär sind.Math. Shornik N. S. vol. 6 (1938) pp. 95–138 (Russian).

    MathSciNet  Google Scholar 

  13. Nevanlinna, F. and Nieminen, T., Das Poisson-Stieltjes'sche Integral und seine Anwendung in der Spektraltheorie des Hilbert'schen Raumes.Ann. Acad. Sci. Fennicae 207 (1955) pp. 1–38.

    Google Scholar 

  14. Nevanlinna, Rolf, Eindeutige Analytische Funktionen, Berlin 1936.

  15. Plessner, A., Zur Theorie der conjugierten trigonomentrischen Reihen. Giessen, 1922.

  16. Pollard, S., Extension to Stieltjes Integrals of a theorem due to Plessner.Journ. London math. Soc. vol. 2 (1927) pp. 37–41.

    Article  Google Scholar 

  17. Riesz, M., Sur les fonctions conjuguées.Math. Zeit. Vol. 27 (1928), pp. 218–244.

    Article  MathSciNet  Google Scholar 

  18. Titchmarsh, E. C., On Conjugate Functions.Proc. London Math. Soc. Vol. 29 (1929) pp. 49–80.

    Article  Google Scholar 

  19. Verblunsky, S., Two moment problems for bounded functions.Proc. Camb. Phil. Soc. Vol. 42 (1946) pp. 189–196.

    MATH  MathSciNet  Google Scholar 

  20. Verblunsky, S., On the initial moments of a bounded function.Proc. Camb. Phil. Soc. Vol. 43 (1947) pp. 275–279.

    Article  MATH  MathSciNet  Google Scholar 

  21. Wolff, Julius and de Kock, F., Les fonctions holomorphes à partie réelle positive et l'intégrale de Stieltjes.Bull. Soc. Math. France Vol. 60 (1932) pp. 221–227.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Paper written under contract with Office of Naval Research, Contract N-ont 583 (04).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aronszajn, N., Donoghue, W.F. On exponential representations of analytic functions in the upper half-plane with positive imaginary part. J. Anal. Math. 5, 321–388 (1956). https://doi.org/10.1007/BF02937349

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02937349

Keywords

Navigation