On the excess of complex exponential systems in \(L^2(-a,a)\). (English) Zbl 1083.30002

A new criterion is given for two complex sequences to have the same excess in the sense of Paley and Wiener in \(L^2(-a,a)\). The author also presents some corollaries and several other results on the excess of complex sequences.


30B60 Completeness problems, closure of a system of functions of one complex variable
42C30 Completeness of sets of functions in nontrigonometric harmonic analysis
Full Text: DOI


[1] Boas, R.P., Entire functions, (1954), Academic Press New York
[2] Boas, R.P., Representations for entire functions of exponential type, Ann. of math., 39, 269-286, (1938) · Zbl 0019.12502
[3] A. Boivin, H. Zhong, Completeness of systems of complex exponentials and the Lambert W functions, preprint, 35 p · Zbl 1210.42046
[4] Khabibullin, B.N., Stability of the completeness of exponential systems on convex compact sets in C, Math. notes, 72, 542-550, (2002) · Zbl 1037.30004
[5] Levin, B.Ya., Distribution of zeros of entire functions, (1964), Amer. Math. Soc. Providence, RI · Zbl 0152.06703
[6] Levin, B.Ya., Lectures on entire functions, (1996), Amer. Math. Soc. Providence, RI · Zbl 0856.30001
[7] Levinson, N., Gap and density theorems, Amer. math. soc. colloq. publ., vol. 26, (1940), Amer. Math. Soc. New York · JFM 66.0332.01
[8] Redheffer, R.M., Completeness of sets of complex exponentials, Adv. math., 24, 1-62, (1977) · Zbl 0358.42007
[9] Redheffer, R.M.; Young, R.M., Completeness and basis properties of complex exponentials, Trans. amer. math. soc., 277, 93-111, (1983) · Zbl 0513.42011
[10] Fujii, N.; Nakamura, A.; Redheffer, R.M., On the excess of sets of complex exponentials, Proc. amer. math. soc., 127, 1815-1818, (1999) · Zbl 0920.30007
[11] Sedletskii, A.M., Excesses of systems of exponential functions, Math. notes, 22, 941-948, (1977)
[12] Sedletskii, A.M., Excesses of systems, close to one another, of exponentials in \(L^P\), Siberian math. J., 24, 626-635, (1983) · Zbl 0535.42022
[13] Sedletskii, A.M., On completeness of the systems \(\{\exp(i x(n + i h_n)) \}\), Anal. math., 4, 125-143, (1978)
[14] Sedletskii, A.M., Nonharmonic analysis, J. math. sci., 116, (2003) · Zbl 1051.42018
[15] Young, R.M., An introduction to non harmonic Fourier series, (2001), Academic Press New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.