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A simple construction of exponential bases in L2 of the union of several intervals

Published online by Cambridge University Press:  20 January 2009

Kristian Seip
Kristian Seip
Affiliation:
Department of Mathematical SciencesNorwegian Institute of TechnologyN-7034 Trondheim, Norway E-mail: seip@imf.unit.no
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Abstract

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It is proved that every space L2 (I1, ∪ I2), where I1 and I2 are finite intervals, has a Riesz basis of complex exponentials , {λk} a sequence of real numbers. A partial result for the corresponding problem for n≧3 finite intervals is also obtained.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 1 , February 1995 , pp. 171 - 177
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Avdonin, S. A., On the question of Riesz bases of complex exponential functions in L2, Vestnik Leningrad Univ. Ser. Mat. 13 (1974); English transl. in Vestnik Leningrad Univ. Ser. Math. 7 (1979), 5–12.Google Scholar
2.Bezuglaya, L. and Katsnelson, V., The sampling theorem for functions with limited multi-band spectrum. I, Z. Anal. Anwendungen 12 (1993), 511–534.CrossRefGoogle Scholar
3.Khrushchev, S. V., Nikol'skii, N. K. and Pavlov, B. S., Unconditional bases of complex exponentials and of reproducing kernels, in Complex Analysis and Spectral Theory (Seminar, Leningrad 1979/80, ed. Havin, V. P. and Nikol'skii, N. K., Lecture Notes in Math. 864, Springer-Verlag, Berlin Heidelberg, 1981), 214–336.Google Scholar
4.Kohlenberg, A., Exact interpolation of band-limited functions, J. Appl. Phys. 24 (1953), 1432–1436.CrossRefGoogle Scholar
5.Landau, H. J., Sampling, data transmission, and the Nyquist rate, Proc. IEEE 55 (1967), 1701–1706.CrossRefGoogle Scholar
6., Yu. I. Lyubarskii, Private Communication, 1993.Google Scholar
7.Paley, R. E. A. C. and Wiener, N., Fourier Transforms in the Complex Domain (Amer. Math. Soc. Colloq. Publ., 19, Amer. Math. Soc., New York, 1934).Google Scholar
8.Pavlov, B., Basicity of an exponential system and Muckenhoupt's condition, Soviet Math. Dokl. 20(1979), 655–659.Google Scholar
9.Young, R. M., An Introduction to Nonharmonic Fourier Series (Academic Press, New York, 1980).Google Scholar