International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 45

The eigenvalues of the Hermitian form are defined as the real roots of the characteristic equation . They will be denoted by
It is easily shown that if for all x, then for all n and all . As these bounds, and the distribution of the within these bounds, can be made more precise by introducing two new notions.
We may now state an important theorem of Szegö (1915, 1920). Let , and put , . If m and M are finite, then for any continuous function defined in the interval [m, M] we haveIn other words, the eigenvalues of the and the values of f on a regular subdivision of ]0, 1[ are equally distributed.
Further investigations into the spectra of Toeplitz matrices may be found in papers by Hartman & Wintner (1950, 1954), Kac et al. (1953), Widom (1965), and in the notes by Hirschman & Hughes (1977).
References
Hartman, P. & Wintner, A. (1950). On the spectra of Toeplitz's matrices. Am. J. Math. 72, 359–366.Hartman, P. & Wintner, A. (1954). The spectra of Toeplitz's matrices. Am. J. Math. 76, 867–882.
Hirschman, I. I. Jr & Hughes, D. E. (1977). Extreme Eigenvalues of Toeplitz Operators. Lecture Notes in Mathematics, Vol. 618. Berlin: SpringerVerlag.
Kac, M., Murdock, W. L. & Szegö, G. (1953). On the eigenvalues of certain Hermitian forms. J. Rat. Mech. Anal. 2, 767–800.
Szegö, G. (1915). Ein Grenzwertsatz uber die Toeplitzschen Determinanten einer reellen positiven Funktion. Math. Ann. 76, 490–503.
Szegö, G. (1920). Beitrage zur Theorie der Toeplitzchen Formen (Erste Mitteilung). Math. Z. 6, 167–202.
Widom, H. (1965). Toeplitz matrices. In Studies in Real and Complex Analysis, edited by I. I. Hirschmann Jr, pp. 179–209. MAA Studies in Mathematics, Vol. 3. Englewood Cliffs: PrenticeHall.