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Mercerian theorems involving Cesaro means of positive order. (English) Zbl 0515.40002


MSC:

40E99 Inversion theorems
40G05 Cesàro, Euler, Nörlund and Hausdorff methods
30C20 Conformal mappings of special domains
33B15 Gamma, beta and polygamma functions
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References:

[1] Agnew, R. P.: Convergence fields of methods of summability. Annals Math.46, 93-101 (1945). · Zbl 0060.16009
[2] Beekmann, W.: Mercer-S?tze f?r abschnittsbeschr?nkte Matrixtransformationen. Math. Z.97, 154-157 (1967). · Zbl 0144.05403
[3] Jakimovski, A.: Some relations between the methods of summability of Abel, Borel, Ces?ro, H?lder and Hausdorff. J. d’Anal. Math.3, 346-381 (1953/54).
[4] Knopp, K.: Theorie und Anwendung der unendlichen Reihen, 5. Aufl. Berlin-G?ttingen-Heidelberg-New York: Springer. 1964. · Zbl 0124.28302
[5] Kuttner, B.: Mercerian theorems involving Ces?ro or H?lder means of any positive order. J. Indian Math. Soc.34, 151-158 (1970). · Zbl 0233.40009
[6] Love, E. R.: Mercer’s summability theorem. J. London Math. Soc.27, 413-428 (1952). · Zbl 0047.30202
[7] Nehari, Z.: Conformal Mapping. New York: McGraw-Hill. 1952. · Zbl 0048.31503
[8] Pitt, H. R.: Mercerian theorems. Proc. Camb. Phil. Soc.34, 510-520 (1938). · JFM 64.0182.01
[9] Polniakowski, Z.: Polynomial Hausdorff transformations, I. Mercerian theorems. Ann. Polonici Math.5, 1-24 (1958). · Zbl 0082.27401
[10] Sz?sz, P.: On Mercer’s theorem for (C, 2)-means. Mh. Math.81, 149-152 (1976). · Zbl 0321.40004
[11] Whittaker, E. T., Watson, G. N.: Modern Analysis. 4th Ed. Cambridge: Univ. Press. 1963. · Zbl 0108.26903
[12] Wilansky, A.: Functional Analysis. New York: Blaisdell. 1964. · Zbl 0136.10603
[13] Zeller, K., Beekmann, W.: Theorie der Limitierungsverfahren. Berlin-Heidelberg-New York: Springer. 1970. · Zbl 0199.11301
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