Bulletin of the American Mathematical Society

MathSciNet review: 1567908
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Book Information:

Author: Paul Koosis
Title: The logarithmic integral
Additional book information: Cambridge Studies In Advanced Mathematics, vol. 12, Cambridge University Press, Cambridge, New York, New Rochelle, Melbourne, Sydney, 1988, xvi + 606 pp., $89.50. ISBN 0-521-30906-9.

[1] S. N. Bernstein, Lecons sur les propriétés extrémales et la meilleure approximation des fonctions analytiques d'une variable réelle, Paris, 1926.

[2] A. Beurling, Quasianalyticity and general distributions, lecture notes, Stanford, 1961.

[3] A. Beurling, Collected works, vol. 1, Birkhäuser, Boston, 1989.

G. G. Bilodeau, The origin and early development of nonanalytic infinitely differentiable functions, Arch. Hist. Exact Sci. 27 (1982), no. 2, 115–135. MR 677684, DOI 10.1007/BF00348345

[5] E. Borel, Lecons sur les fonctions monogènes uniformes d'une variable complexe, Gauthier-Villars, Paris, 1917.

James E. Brennan, Functions with rapidly decreasing negative Fourier coefficients, Complex analysis, I (College Park, Md., 1985–86) Lecture Notes in Math., vol. 1275, Springer, Berlin, 1987, pp. 31–43. MR 922291, DOI 10.1007/BFb0078343

[7] T. Carleman, Les fonctions quasi-analytiques, Gauthier-Villars, Paris, 1926.

Arnaud Denjoy, Les fonctions quasi-analytiques, C. R. Acad. Sci. Paris 242 (1956), 581–586 (French). MR 74471

Bent Fuglede, Fine potential theory—a survey, Mitt. Math. Ges. DDR 2-3 (1986), 3–21. MR 877269, DOI 10.1016/0010-4485(85)90272-6

[10] J. Hadamard, Sur la généralisation de la notion de fonction analytique, C. R. Seanches Soc. Math. France (1912), 28-29.

W. K. Hayman, Subharmonic functions. Vol. 2, London Mathematical Society Monographs, vol. 20, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1989. MR 1049148

[12] E. Holmgren, Sur l'équation de la propagation de la chaleur, Ark. Mat. Astronom. Fys. 4 (14), (1908), 1-11, and 4 (18), (1908), 1-28.

[13] E. Holmgren, Sur les solutions quasianalytiques de l'équation de la chaleur, Ark. Mat. Astronom. Fys. 18 (1924), 1-9.

Fritz John, Partial differential equations, 3rd ed., Applied Mathematical Sciences, vol. 1, Springer-Verlag, New York-Berlin, 1978. MR 514404

Norman Levinson, Gap and Density Theorems, American Mathematical Society Colloquium Publications, Vol. 26, American Mathematical Society, New York, 1940. MR 0003208

[16] A. Tychonoff, Théorèmes d'unicité pour l'équation de la chaleur, Mat. Sb. 42(1935), 199-216.

[17] S. Täcklind, Sur les classes quasianalytiques des solutions des équations aux derivees partiélles du type parabolique, Nova Acta Soc. Sci. Upsal. 10 (1936), 1-57.

I. N. Vekua, Generalized analytic functions, Pergamon Press, London-Paris-Frankfurt; Addison-Wesley Publishing Company, Inc., Reading, Mass., 1962. MR 0150320

A. L. Vol′berg, Summability of the logarithm of a quasi-analytic function, Dokl. Akad. Nauk SSSR 265 (1982), no. 6, 1297–1302 (Russian). MR 670692

A. A. Borichev and A. L. Vol′berg, Uniqueness theorems for almost analytic functions, Algebra i Analiz 1 (1989), no. 1, 146–177 (Russian); English transl., Leningrad Math. J. 1 (1990), no. 1, 157–191. MR 1015338

Michael Benedicks, The support of functions and distributions with a spectral gap, Math. Scand. 55 (1984), no. 2, 285–309. MR 787203, DOI 10.7146/math.scand.a-12082

[1] S. N. Bernstein, Lecons sur les propriétés extrémales et la meilleure approximation des fonctions analytiques d'une variable réelle, Paris, 1926.




[2] A. Beurling, Quasianalyticity and general distributions, lecture notes, Stanford, 1961.




[3] A. Beurling, Collected works, vol. 1, Birkhäuser, Boston, 1989.




[4] G. G. Bilodeau, The origin and early development of non-analytic infinitely differentiable functions, Arch. Hist. Exact Sci. 27 (1982), 115-135. MR 0677684




[5] E. Borel, Lecons sur les fonctions monogènes uniformes d'une variable complexe, Gauthier-Villars, Paris, 1917.




[6] J. Brennan, Functions with rapidly decreasing negative Fourier coefficients, Lecture Notes in Math., vol. 1275, Springer-Verlag, Berlin, 1987, pp. 31-43. MR 922291




[7] T. Carleman, Les fonctions quasi-analytiques, Gauthier-Villars, Paris, 1926.




[8] A. Denjoy, Sur les fonctions quasi-analytiques de variable réelle, C. R. Acad. Sci. Paris Ser. 1 Math. 173 (1921), 1329-1331. MR 74471




[9] B. Fuglede, Fine potential theory - a survey, lecture, Rostock, 1986. MR 877269




[10] J. Hadamard, Sur la généralisation de la notion de fonction analytique, C. R. Seanches Soc. Math. France (1912), 28-29.




[11] W. K. Hayman, Subharmonic functions, vol. 2, Academic Press, London, 1989. MR 1049148




[12] E. Holmgren, Sur l'équation de la propagation de la chaleur, Ark. Mat. Astronom. Fys. 4 (14), (1908), 1-11, and 4 (18), (1908), 1-28.




[13] E. Holmgren, Sur les solutions quasianalytiques de l'équation de la chaleur, Ark. Mat. Astronom. Fys. 18 (1924), 1-9.




[14] F. John, Partial differential equation, 4th ed., Springer-Verlag, Berlin, 1982. MR 514404




[15] N. Levinson, Gap and density theorems, Amer. Math. Soc. Colloq. Publ., vol. 26, Amer. Math. Soc., New York, 1940. MR 3208




[16] A. Tychonoff, Théorèmes d'unicité pour l'équation de la chaleur, Mat. Sb. 42(1935), 199-216.




[17] S. Täcklind, Sur les classes quasianalytiques des solutions des équations aux derivees partiélles du type parabolique, Nova Acta Soc. Sci. Upsal. 10 (1936), 1-57.




[18] I. N. Vekua, Generalized analytic functions, Addison-Wesley, Reading, Mass., 1962. MR 150320




[19] A. L. Vol'berg, The logarithm of an almost analytic function is summable, Dokl. Akad. Nauk SSSR 265 (1982), 1297-1301. MR 670692




[20] A. A. Borichev and A. L. Vol'berg, Uniqueness theorems for almost analytic functions, Algebra and Analysis 1 (1989), 144-176. MR 1015338




[21] M. Benedicks, The support of functions and distributions with a spectral gap, Math. Scand. 55 (1984), 285-309. MR 787203