References
B. Berndtsson, Note on Pavlov-Korevaar-Dixon interpolation,Nederl. Akad. Wetensch. Proc. Ser. A,81 (1978).
J. A. Clarkson-P. Erdös, Approximation by polynomials,Duke Math. J.,10 (1943), 5–11.
M. Dixon—J. Korevaar, Nonspanning sets of powers on curves: analyticity theorem,Duke Math. J.,45 (1978).
T. Erkama, Classes non quasi-analytiques et le théorème d'approximation de Müntz,C. R. Acad. Sci. Paris Sér. A,283 (1976), 595–597.
J. Korevaar, Approximation on curves by linear combinations of exponentials. In:Approximation Theory (editor G. G. Lorentz). Acad. Press (New York, 1973), pp. 387–393.
J. Korevaar—M. Dixon, Interpolation, strongly nonspanning powers and Macintyre exponents,Nederl. Akad. Wetensch. Proc. Ser. A,81 (1978).
T. Kővári, A gap theorem for entire functions of infinite order,Michigan Math. J.,12 (1965), 133–140.
A. F. Leont'ev, On the completeness of a system of exponentials on a curve (Russian),Sibirsk. Mat. Z.,15 (1974), 1103–1114.
W. Luxemburg-J. Korevaar, Entire functions and Müntz-Szász type approximation,Trans. Amer. Math. Soc.,157 (1971), 23–37.
A. J. Macintyre, Asymptotic paths of integral functions with gap power series.Proc. London Math. Soc., (3)2 (1952), 286–296.
P. Malliavin-J. A. Siddiqi, Approximation polynomiale sur un arc analytique dans le plan complexe,C. R. Acad. Sci. Paris Sér. A,273 (1971), 105–108.
P. Malliavin-J. A. Siddiqi, Classes de fonctions monogènes et approximation par des sommes d'exponentielles sur un arc rectifiable deC, C. R. Acad. Sci. Paris Sér. A,282 (1976), 1091–1094.
C. H. Müntz, Über den Approximationssatz von Weierstrass. In:H. A. Schwarz Festschrift, (Berlin, 1914), pp. 303–312.
A. I. Pavlov Growth along curves of entire functions specified by gap power series (Russian),Sibirsk. Mat. Z.,13 (1972), 1169–1181.
L. Schwartz, Étude des sommes d'exponentielles réelles,Actualités Sci. Indust.,959 Hermann (Paris, 1943).
O. Szász, Über die Approximation stetiger Funktionen durch lineare Aggregate von Potenzen,Math. Ann.,77 (1915), 482–496.
J. L. Walsh, Über die Entwicklung einer Funktion einer komplexen Veränderlichen nach Polynomen,Math. Ann.,96 (1927), 437–450.
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Dedicated to Professor G. Alexits on his eightieth birthday
Work of second author supported by a grant from the Netherlands' research organization Z. W. O.
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Korevaar, J., Dixon, M. Nonspanning sets of exponentials on curves. Acta Mathematica Academiae Scientiarum Hungaricae 33, 89–100 (1979). https://doi.org/10.1007/BF01903384
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DOI: https://doi.org/10.1007/BF01903384