On some non-archimedean normed linear spaces. I
Compositio Mathematica, Tome 19 (1968) no. 1, p. 1-15
@article{CM_1968__19_1_1_0,
     author = {Robert, Pierre},
     title = {On some non-archimedean normed linear spaces. I},
     journal = {Compositio Mathematica},
     publisher = {P. Noordhoff N. V., Groningen},
     volume = {19},
     number = {1},
     year = {1968},
     pages = {1-15},
     zbl = {0153.44101},
     mrnumber = {226368},
     language = {en},
     url = {http://www.numdam.org/item/CM_1968__19_1_1_0}
}
Robert, Pierre. On some non-archimedean normed linear spaces. I. Compositio Mathematica, Tome 19 (1968) no. 1, pp. 1-15. http://www.numdam.org/item/CM_1968__19_1_1_0/

M.G. Arsove, [1] The Paley-Wiener Theorem in metric linear spaces, Pacific J. Math., 10 (1960) pp. 365-379. | MR 125429 | Zbl 0097.09301

C.W. Clenshaw, [2] The numerical solution of linear differential equations in Chebyshev series, Proc. Camb. Phil. Soc., 53 (1957) pp. 134-149. | MR 82196 | Zbl 0077.32503

I.S. Cohen, [3] On non-Archimedean normed spaces, Proc. Kon. Ned., Akad. Wet., 51 (1948) pp. 693 - 698. | MR 25683 | Zbl 0030.26001

H.F. Davis, [4] A note on asymptotic series, Can. J. Math., 9 (1957) pp. 90-95. | MR 92029 | Zbl 0091.05906

J. De Groot [5] Non-Archimedean metrics in topology, Proc. Amer. Math. Soc., 7 (1956) pp. 948-953. | MR 80905 | Zbl 0072.40201

V.A. Ditkin and A.P. Prudnikov, [6] "Operational Calculus in two variables and its applications", (English translation by D. M. G. Wishart), Pergamon Press, New York, 1962. | MR 138957 | Zbl 0116.30902

N. Dunford and J.T. Schwartz, [7] "Linear Operators, Part I: General Theory", Interscience Publishers Inc., New York, 1958. | MR 1009162 | Zbl 0084.10402

A. Erdélyi et al., [8] "Tables of Integral Transforms", Vol. I and Vol. II, McGraw-Hill Book Co. Inc., New York, 1954. | MR 61695 | Zbl 0058.34103

A. Erdélyi, [9] "Asymptotic Expansions", Dover Publications, Inc., New York, 1956. | MR 78494 | Zbl 0070.29002

A. Erdélyi, [10] General asymptotic expansions of Laplace integrals, Arch. Rat. Mech. Anal., 7 (1961) pp. 1-20. | MR 131128 | Zbl 0097.08802

A. Erdélyi and M. Wyman, [11] The asymptotic evaluation of certain integrals, Arch. Rat. Mech. Anal., 14 (1963) pp. 217-260. | MR 157170 | Zbl 0168.37903

I. Fleischer, [12] Sur les espaces normés non-archimédiens, Proc. Kon. Ned. Akad. Wet. Ser. A, 57 (1956) pp. 165-168. | MR 62338 | Zbl 0055.09903

L. Fox, [13] Chebyshev methods for ordinary differential equations, Computer Jnl., 4 (1961-62) pp. 318-331. | MR 136521 | Zbl 0103.34203

P.R. Halmos, [14] "Introduction to Hilbert spaces", 2nd ed., Chelsea Publ. Co., New York, 1957. | Zbl 0079.12404

T.E. Hull, [15] On some integral equations with unbounded eigenvalues, S.I.A.M. Journal, 7 (1959) pp. 290-297. | MR 108700 | Zbl 0095.08401

W. Hurewicz and H. Wallman, [16] "Dimension Theory", Princeton University Press, Princeton, N. J., 1941. | MR 6493 | Zbl 0060.39808

A.W. Ingleton, [17] The Hahn-Banach Theorem for non-Archimedean valued fields, Proc. Camb. Philo. Soc. 48 (1952) pp. 41-45. | MR 45939 | Zbl 0046.12001

J.L. Kelley, [18] "General topology", D. Van Nostrand Co. Inc., Princeton, N. J., 1955. | MR 70144 | Zbl 0066.16604

A.N. Kolmogorof and S.V. Fomin, [19] "Elements of the Theory of Functions and Functional Analysis", Vol. I and Vol. II (Russian) English translation, Graylock Press, Rochester, N. Y., 1957.

C. Lanczos, [20] Trigonometric interpolation of empirical and analytical functions, J. Math. and Phys., 17 (1938) pp. 123-199. | JFM 64.0577.02 | Zbl 0020.01301

C. Lanczos, [21] "Applied Analysis", Prentice Hall Inc., Englewood Cliffs, N. J., 1956. | MR 84175 | Zbl 0111.12403

L.H. Loomis, [22] "An Introduction to Abstract Harmonic Analysis", D. van Nostrand, Inc., New York, 1953. | MR 54173 | Zbl 0052.11701

J. Mikusiňski, [23] "Operational Calculus", (Translation of the 2nd Polish edition, vol. 30, Monografie Matematyczne, 1957), Pergamon Press, Inc., New York, 1959. | Zbl 0088.33002

A.F. Monna, [24] Sur les espaces linéaires normés, I : Proc. Kon. Ned. Akad. Wet, 49 (1946) pp. 1045-1055; II: Proc. Kon. Ned. Akad. Wet, 49 (1946) pp. 1056-1062; III: Proc. Kon. Ned. Akad. Wet, 49 (1946) pp. 1134-1141; IV: Proc. Kon. Ned. Akad. Wet, 49 (1946) pp. 1142-1152; V: Proc. Kon. Ned. Akad. Wet, 51 (1948) pp. 197- 210; VI: Proc. Kon. Ned. Akad. Wet, 52 (1949) pp. 151- 160. | Zbl 0031.36101

A.F. Monna, [25] Sur les espaces normés non-archimédiens, I: Proc. Kon. Ned. Akad. Wet, Ser. A, 59 (1956) pp. 475-483; II: Proc. Kon. Ned. Akad. Wet, Ser. A, 59 (1956) pp. 484-489; III: Proc. Kon. Ned. Akad. Wet, Ser. A, 60 (1957) pp. 459-467; IV: Proc. Kon. Ned. Akad. Wet, Ser. A, 60 (1957) pp. 468-476. | MR 80882 | Zbl 0080.31404

M.A. Naimark, [26] "Normed rings", (English translation of the first Russian ed. by L. F. Boron), P. Noordhoff N.V., Groningen, Netherland, 1959. | MR 110956 | Zbl 0137.31703

R.E.A.C. Paley and N. Wiener, [27] "Fourier Transforms in the Complex Domain", Amer. Math. Soc. Colloquium Publ. no. 19, New York, 1934. | MR 1451142 | Zbl 0011.01601

L. Pontrjagin, [28] "Topological Groups", English translation, Princeton Univ. Press, Princeton, N. J., 1946. | JFM 65.0872.02

J. Popken, [29] Asymptotic expansions from an algebraic standpoint, Proc. Kon. Ned. Akad. Wet, Ser. A, 56 (1953) pp. 131-143. | MR 56114 | Zbl 0051.04803

F.W. Schafke, [30] Das Kriterium von Paley und Wiener in Banaschem Raum, Math. Nach., 3 (1949) pp. 59-61. | MR 34524 | Zbl 0035.19701

O.F.G. Schilling, [31] "The Theory of Valuations", Mathematical Surveys, No. IV, Amer. Math. Soc., 1950. | MR 43776 | Zbl 0037.30702

M. Schulzer, [32] "Asymptotic Properties of Solutions of Equations in Banach Spaces" , M.A. Thesis, University of British Columbia, Vancouver, 1959.

C.A. Swanson and M. Schulzfr, [33] Asymptotic solutions of equations in Banach spaces, Can. J. of Math., 13 (1961) pp. 493-504. | MR 123928 | Zbl 0202.42802

C.A. Swanson, [34] An inequality for linear transformations with eigenvalues, Bull. Amer. Math. Soc., 67 (1961) pp. 607-608. | MR 131774 | Zbl 0102.32601

C.A. Swanson, [35] On spectral estimation, Bull. Amer. Math. Soc., 68 (1962) pp. 33-35. | MR 133014 | Zbl 0102.32602

A.E. Taylor, [36] "Introduction to Functional Analysis", J. Wiley and Sons, Inc., New York, 1958. | MR 98966 | Zbl 0081.10202

J. Todd, [37] "Introduction to the Constructive Theory of Functions", International Series of Numerical Mathematics, Vol. I, Academic Press Inc., New York, 1963. | MR 156129

J.G. Van Der Corput, [38] "Asymptotic Expansions I. Fundamental Theorems of Asymptotics" , University of California, Berkeley, 1954.

J.G. Van Der Corput, [39] Asymptotics. I, Proc. Kon. Ned. Akad. Wet, Ser. A, 57 (1954) pp. 206-217. | MR 66477 | Zbl 0059.05101

B.L. Van Der Waerden, [40] "Modern Algebra", Vol. I, Revised English edition, Frederick Ungar Publ. Co., New York, 1953.

D.V. Widder, [41] "The Laplace Transform", Princeton University Press, Princeton, N. J., 1941. | JFM 67.0384.01 | MR 5923 | Zbl 0063.08245