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References
Edrei, A.: On the generating functions of totally positive sequences. J. Analyse math. 2, 104–109 (1952).
Gantmacher, F., and M. Krein: Oscillation matrices and vibrations of mechanical systems. Moscow 1950.
Harris, T. E.: The theory of branching processes. Berlin-Göttingen-Heidelberg: Springer 1963.
Ito, K., and H. P. McKean: Diffusion processes and their sample paths. New York: Academic Press 1965.
Karlin, S.: Total positivity, absorption probabilities and applications. Trans. Amer. math. Soc. 111, 34–107 (1964).
—: The existence of eigenvalues for integral operators. Trans. Amer. math. Soc. 113, 1–17 (1964).
—, and J. L. McGregor: Random walks. Illinois J. Math. 3, 1141–1164 (1959).
- - Uniqueness of stationary measures for branching processes and applications, to appear in Proc. 5th Berkeley Sympos. math. Statist. Probab. 1965.
— —: Spectral representation of branching processes, II. Case of continuous spectrum. Z. Wahrscheinlichkeitstheorie verw. Geb. 5, 34–54 (1966).
- - Spectral representation for continuous time branching processes (to be published).
Kendall, D.: Integral representations for Markov transition probabilities. Bull. Amer. math Soc. 64, 358–362 (1958).
—: On super critical branching processes with a positive chance of extinction. To appear in Festschrift Volume in honor of J. Neyman. New York: J. Wiley 1966.
McKean, H. P.: Elementary solutions for certain parabolic partial differential equations. Trans. Amer. math. Soc. 82, 519–548 (1956).
Titchmarsh, E. C.: The theory of functions. London: Oxford University Press 1939.
Karlin, S.: Total positivity and applications. Stanford University Press 1967.
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Research supported in part by Contracts ONR 225(28) and NIH USPHS 10452 at Stanford University.
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Karlin, S., McGregor, J. Spectral theory of branching processes. I. Z. Wahrscheinlichkeitstheorie verw Gebiete 5, 6–33 (1966). https://doi.org/10.1007/BF00532810
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DOI: https://doi.org/10.1007/BF00532810