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An optimal spectral estimator for multi-dimensional time series with an infinite number of sample points

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References

  1. Agmons, S.: Lectures on elliptic boundary value problems Math. Studies2. London: van Nostrand 1965

    Google Scholar 

  2. Arnold, L.: Stochastic differential equations. New York: Wiley & Sons 1974

    Google Scholar 

  3. Aronszajn, A.: Theory of reproducing kernels. Trans. Amer. Math. Soc.68, 337–404 (1950)

    Google Scholar 

  4. Brillinger, D.R.: Time series, data analysis and theory. New York: Holt, Rinehardt & Winston 1965

    Google Scholar 

  5. Deley, G.W.: Waveform design. In: Radar Handbook. New York: McGraw Hill 1970

    Google Scholar 

  6. Donoghue, W.F.: Continuous function spaces isometric to Hilbert space. Proc. Amer. Math. Soc.8, 1–2 (1957)

    Google Scholar 

  7. Dym, H., McKean, H.P.: Fourier series and integrals. New York: Academic Press 1972

    Google Scholar 

  8. Gantmacher, F.R.: The theory of matrices1. New York: Chelsea 1959

    Google Scholar 

  9. Gordon, W.B.: Accuracy of linear spectral estimates of band-limited signals. J. Time Ser. Anal.2, 173–184 (1981).

    Google Scholar 

  10. Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  11. Kato, T.: Perturbation theory for linear operators, 2nd ed. Grundlehren Math. Wiss.132. New York-Heidelberg-Berlin: Springer 1980

    Google Scholar 

  12. Katznelson, Y.: An introduction to harmonic analysis. New York: Dover 1976

    Google Scholar 

  13. Moore, E.H.: See reference 3

    Google Scholar 

  14. Nelson, E.: Kernel functions and eigenfunction expansions. Duke Math. J.25, 15–27 (1958)

    Google Scholar 

  15. Robinson, D.W.: The thermodynamic pressure in quantum statistical mechanics. Lecture Notes in Phys.9. Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

  16. Rostamian, R.: Continuity properties of stationary points of quadratic functionals in Hilbert space. Numer. Funct. Anal. Optim.3, 147–167 (1981).

    Google Scholar 

  17. Rudin, W.: Fourier analysis on groups. New York: Wiley-Interscience 1962

    Google Scholar 

  18. Shannon, C.E.: Communication in the presence of noise. Proc. I.R.E.37, 10–21 (1949).

    Google Scholar 

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  1. Department of Mathematics, University of Pennsylvania, 19104, Philadelphia, PA, USA

    Palle E. T. Jørgensen

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  1. Palle E. T. Jørgensen
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Jørgensen, P.E.T. An optimal spectral estimator for multi-dimensional time series with an infinite number of sample points. Math Z 183, 381–398 (1983). https://doi.org/10.1007/BF01176479

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  • DOI: https://doi.org/10.1007/BF01176479

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