Abstract
Some recent results concerning theL-problem of moments in two variables are related via the Fourier-Laplace transform to an interpolation problem in the tube domain over a quadrant inR 2. The class of analytic functions for which the interpolation problem is posed is identified with the symbols of all bounded analytic Wiener-Hopf operators acting on theH 2-Hardy space of the tube domain. The extremal solutions of the corresponding truncated problem are computed and the related uniqueness phenomenon is also discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akhiezer, N.I.: Krein, M.G.,Some questions in the theory of moments, Transl. Math. Mono. vol. 2, Amer. Math. Soc., Providence, R.I., 1962.
Bergman, S.,The kernel function and conformal mapping, Math. Surv. Mono. vol. 5, Amer. Math. Soc, Providence, R.I., 1950.
Bochner, S.,Harmonic analysis and the theory of probability, Univ. Calif. Press., Berkeley, 1955.
Bergman, S.; Martin, T.W., A modified moment problem in two variables, Duke Math.J., 6(1940), 389–407.
Krein, M.G.; Nudelman, A.A.,Markov moment problem and extremal problems, Transl. Math. Mono, vol. 50, Amer. Math. Soc., Providence, R.I., 1977.
Martin, M.; Putinar, M.,Lectures on hyponormal operators, Birkhäuser Verlag, Basel, 1989.
Paley, R.E.A.C.; Wiener, N.,Fourier transforms in the complex domain, Colloq. Publ. vol. 19, Amer. Math. Soc., Providence, R.I., 1934.
Putinar, M., TheL-problem of moments in two variables, J. Funct. Analysis 94(1990), 288–307.
Putinar, M., Extremal solutions of the two-dimensionalL-problem of moments, J. Funct. Analysis 136(1996), 331–364.
Shapiro, H.S.,The Schwarz function and its generalization to higher dimensions, Univ. Arkansas Lect. Notes Math. vol. 9, J. Wiley and Sons, New York, 1992.
Stein, E.; Weiss, G.,Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, 1971.
Widder, D.V., The inversion of the Laplace integral and the related moment problem, Trans. Amer. Math. Soc. 36(1934), 107–200.