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References
Borwein, D.: On products of sequences. J. London math. Soc. 33, 352–357 (1958).
Brudno, A.: Summation of bounded sequences by matrices. Mat. Sbornik, n. Ser. 16, 191–247 (1945).
Cooke, R.G.: Infinite matrices and sequence spaces. London: Macmillan 1950.
Garabedian, H.L., Randels, W.C.: Theorems on Riesz means. Duke math. J. 4, 529–533 (1938).
Hardy, G.H.: Divergent series. London: Oxford Press 1949.
Kaluza, T.: über die Koeffizienten reziproker Potenzreihen. Math. Z. 28, 161–170 (1928).
Karlin, S., McGregor, J.: Random walks. Illinois J. Math. 3, 66–81 (1959).
Kemeny, J.G.: Representation theory for denumerable Markov chains. Trans. Amer. math. Soc. 125, 47–62 (1966).
—: Slowly spreading chains of the first kind. J. math. Analysis Appl. 15, 295–310 (1966).
—, Snell, J.L., Knapp, A.W.: Denumerable Markov chains. Princeton, N.J.: Van Nostrand 1966.
Mazur, S.: Eine Anwendung der Theorie der Operationen bei der Untersuchung der Toeplitzschen Limitierungsverfahren. Studia math. 2, 40–50 (1930).
Rényi, A.: Summation methods and probability methods. Publ. math. Inst. Hungar. Acad. Sci. 4, 389–397 (1959).
Schmetterer, L.: Wahrscheinlichkeitstheoretische Bemerkungen zur Theorie der Reihen. Arch. der Math. 14, 311–316 (1963).
Spitzer, F.L.: Principles of random walk. Princeton, N.J.: Van Nostrand 1964.
Zeller, K.: Theorie der Limitierungsverfahren. Berlin-Göttingen-Heidelberg: Springer 1958.
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The preparation of this paper was aided by the National Science Foundation.
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Kemeny, J.G., Snell, J.L. Markov chains and summability methods. Z. Wahrscheinlichkeitstheorie verw Gebiete 18, 17–33 (1971). https://doi.org/10.1007/BF00538485
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DOI: https://doi.org/10.1007/BF00538485