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Electrostatic instabilities of a uniform non-Maxwellian plasma. (English) Zbl 0090.22801

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[1] Vlasov, Zhur. Eksp. i Teoret. Fiz. 8 pp 291– (1938)
[2] Bernstein, Phys. Rev. 109 pp 10– (1958)
[3] Buneman, Phys. Rev. Letters 1 pp 8– (1958)
[4] Auer, Phys. Rev. Letters 1 pp 411– (1958)
[5] Kahn, Astrophys. J. 129 pp 468– (1959)
[6] S. G. Mikhlin,Integral Equations(Pergamon Press, London, England, 1957), pp. 115–116. Theorems 1 and 3 of this reference show that Z(\(\xi\)+i0) is bounded and continuous, since the boundedness of Gi imply a Lipschitz condition on F(u).
[7] Harris, Phys. Rev. Letters 2 pp 34– (1959)
[8] Van Kampen, Physica 21 pp 949– (1955)
[9] E. T. Copson,Theory of Functions of a Complex Variable(Oxford University Press, Oxford, England, 1935), p. 119. · Zbl 0012.16902
[10] W. K. Hayman (private communication, 1959).
[11] S. Tamor (unpublished) and others have obtained similar criteria.
[12] E. C. Titchmarsh,Theory of Fourier Integrals, (Oxford University Press, Oxford, England, 1937), pp. 311–312.
[13] Landau, J. Phys. (U.S.S.R.) 10 pp 25– (1946)
[14] van Kampen, Physica 21 pp 949– (1955)
[15] See reference 11, pp. 115–116, Theorem (84), with the following modifications: p = p = 2, \(\alpha\) = \(\beta\) = 1, f(x+h)-f(x-h)hf(x), sin xhh.
[16] R. E. A. C. Paley and N. Wiener,Fourier transforms in the complex domain(American Mathematical Society Colloquim Publications, New York, 1934), Vol. XIX, Sec. 18. · Zbl 0011.01601
[17] See reference 11, p. 11 (Theorem 1).
[18] Bohm, Phys. Rev. 75 pp 1864– (1949)
[19] Bernstein, Phys. Rev. 108 pp 546– (1957)
[20] Berz, Proc. Phys. Soc. B69 pp 939– (1956) · Zbl 0071.44501 · doi:10.1088/0370-1301/69/9/308
[21] Auer, Phys. Rev. Letters 1 pp 411– (1958)
[22] N. G. van Kampen (see the work cited in footnote 13) has obtained the same result.
[23] Twiss, Phys. Rev. 88 pp 1392– (1952)
[24] Sumi, J. Phys. Soc. Japan 13 pp 1476– (1958)
[25] Harris, Astrophys. J. 108 pp 112– (1948)
[26] S. Tamor (unpublished) has shown for the special case niTe = neTi that the critical value of u2-uI is 0.93(\(\alpha\)1+\(\alpha\)2) without imposing the conditions (29)–(31).
[27] I. Bernstein (unpublished) also obtained this result for Tie.
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