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References
Berndtsson, B.: A note on Pavlov-Korevaar-Dixon interpolation. Nederl. Akad. Wet., Proc., Ser. A 81 (1978), 409–414.
Clarkson, J. A., Erdös, P.: Approximation by polynomials. Duke math. J. 10 (1943), 5–11.
Dixon, M., Korevaar, J.: Nonspanning sets of powers on curves: analyticity theorem. Duke math. J. 45 (1978), 543–559.
Erkama, T.: Classes non quasi-analytiques et le théorème d'approximation de Müntz. C. r. Acad. Sci., Paris, Sér. A 283 (1976), 595–597.
Fuchs, W. H. J.: Proof of a conjecture of G. Pólya concerning gap series. Illinois J. Math. 7 (1963), 661–667.
Ganelius, T., Newman, D.: Müntz-Jackson theorems in all Lp spaces with unrestricted exponents. Amer. J. Math. 98 (1976), 295–309.
Hayman, W. K.: Angular value distribution of power series with gaps. Proc. London Math. Soc., III. Ser. 24 (1972), 590–624.
Korevaar, J.: Approximation on curves by linear combinations of exponentials, in "Approximation theory". Academic Press, New York and London (1973), 387–393.
Korevaar, J., Dixon, M.: Interpolation, strongly nonspanning powers and Macintyre exponents. Nederl. Akad. Wet., Proc., Ser. A 81 (1978), 243–258.
Korevaar, J., Dixon, M.: Nonspanning sets of exponentials on curves. Acta math. Acad. Sci. Hungar. 33 (1979), 89–100.
Kövari, T.: On the asymptotic paths of entire functions with gap power series. J. Analyse math. 15 (1965), 281–286.
Kövari, T.: A gap theorem for entire functions of infinite order. Michigan math. J. 12 (1965), 133–140.
Kövari, T.: On a result of A. J. Macintyre, in "Mathematical essays dedicated to A. J. Macintyre". Ohio University Press, Athens, Ohio (1970), 217–222.
Leont'ev, A. F.: On the completeness of a system of exponentials on a curve (Russian). Sibir. mat. Žurn. 15 (1974), 1103–1114.
Luxemburg, W. A. J., Korevaar, J.: Entire functions and Müntz-Szász type approximation. Trans. Amer. math. Soc. 157 (1971), 23–37.
Macintyre, A. J.: Asymptotic paths of integral functions with gap power series. Proc. London math. Soc., III. Ser. 2 (1952), 286–296.
Malliavin, P., Siddiqi, J. A.: Approximation polynomiale sur un arc analytique dans le plan complexe. C. r. Acad. Sci., Paris, Sér. A 273 (1971), 105–108.
Malliavin, P., Siddiqi, J. A.: Classes de fonctions monogènes et approximation par des sommes d'exponentielles sur un arc rectifiable de ℂ, C. r. Acad. Sci., Paris, Sér. A 282 (1976), 1091–1094.
Müntz, C. H.: Über den Approximationssatz von Weierstrass. H. A. Schwarz Festschrift, Berlin (1914), 303–312.
Pavlov, A. I.: The growth along curves of entire functions that are defined by lacunary power series (Russian). Sibir. mat. Žurn. 13 (1972), 1169–1181.
Pólya, G.: Untersuchungen über Lücken und Singularitäten von Potenzreihen. Math. Z. 29 (1929), 549–640.
Schwartz, L.: Étude des sommes d'exponentielles réelles. Hermann, Paris (1943).
Sons, L. R.: On the Macintyre conjecture. Illinois J. Math. 14 (1970), 613–620.
Sons, L. R.: An analogue of a theorem of W. H. J. Fuchs on gap series. Proc. London math. Soc., III. Ser. 21 (1970), 525–539.
Szász, O.: Über die Approximation stetiger Funktionen durch lineare Aggregate von Potenzen. Math. Ann. 77 (1915), 482–496.
Walsh, J. L.: Über die Entwicklung einer Funktion einer komplexen Veränderlichen nach Polynomen. Math. Ann. 96 (1927), 437–450.
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Korevaar, J. (1979). Müntz approximation on arcs and macintyre exponents. In: Laine, I., Lehto, O., Sorvali, T. (eds) Complex Analysis Joensuu 1978. Lecture Notes in Mathematics, vol 747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063975
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DOI: https://doi.org/10.1007/BFb0063975
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