Voir la notice de l'article provenant de la source Math-Net.Ru
@article{SEMR_2007_4_a12, author = {Victor Katsnelson}, title = {On {H.~Weyl} and {H.~Minkowski} polynomials}, journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a}, pages = {169--237}, publisher = {mathdoc}, volume = {4}, year = {2007}, language = {en}, url = {http://geodesic.mathdoc.fr/item/SEMR_2007_4_a12/} }
Victor Katsnelson. On H.~Weyl and H.~Minkowski polynomials. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 169-237. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a12/
[1] Adler R. J. and J. E. Tailor, Random Fields and Geometry, Springer, 2007 | MR
[2] Alexandrov A. D., Selected Works, v. 1, Gordon and Breach Publishers, Amsterdam, 1996, x+322 pp. | MR | Zbl
[3] Alexandrov A. D., “To the theory of mixed volumes of convex bodies. Part II. New inequalities for mixed volumes and their applications”, 61–97, in [Al] | Zbl
[4] Alexandrov A. D., “To the theory of mixed volumes of convex bodies. Part III. Extension of two Minkowski Theorems on convex polyhedra to all convex bodies”, 99–117, in [Al] | Zbl
[5] Alexandrov A. D., “To the theory of mixed volumes of convex bodies. Part IV. Mixed discriminants and mixed volumes”, 119–144, in [Al] | Zbl | Zbl
[6] Arnold V., “Comments to the Russian translation of the paper”, [Wey1]
[7] Barnes E.W., “The asymptotic expansions of integral functions defined by Taylor's series”, Philosoph. Trans. Royal Soc. London A, 206 (1906), 249–297 | DOI | Zbl
[8] Berger M., Gostiaux B., Differential Geometry, Manifolds, Curves, Surfaces, Springer-Verlag, Berlin, Heidelberg, New York, 1988, xii+474 pp. | MR
[9] Bhattacharyya S. P., Chapellat H., Keel L. H., Robust Control. The parametric Approach, Prentice Hall PTR, Upper Saddle River, NJ, 1995, xiv, 648 pp.
[10] Bonneson T., Fenchel W., Theorie der konvexen Körper, Springer, Berlin, 1934 (In German); Bonnezon T., Fenkhel V., Teoriya vypuklykh tel, Fazis, Moskva, 2002, kh+210 pp.
[11] Busemann H., Convex Surfaces, Interscience, New York, 1958 | MR | Zbl
[12] Burago Yu. D., Zalgaller V. A., Geometric inequalities, Springer-Verlag, Berlin, Heidelberg, 1988, xiv+331 pp. | MR | MR | Zbl | Zbl
[13] Chebotarev N. G., “On entire functions with real interlacing roots”, Doklady AN SSSR, 35 (1942), 219–222 (In Russian) | MR
[14] Craven Th., Csordas G., “Location of zeros. Part I. Real polynomials ans entire functions”, Illinois Journ. of Math., 27:2 (1983), 244–278 | MR | Zbl
[15] Craven Th., Csordas G., “Jensen polynomials and the Turán and Laguerre inequalities”, Pacif. Journ. of Math., 136:2 (1989), 241–260 | MR | Zbl
[16] Craven Th., Csordas G., “Differential operators of infinite order and the distribution of zeros of entire functions”, Jour. Math. Anal. Appl., 186 (1994), 799–820 | DOI | MR | Zbl
[17] Craven Th., Csordas G., “The Fox-Wright functions and Laguerre multiplier sequences”, Journ. of Math. Analysis and Appl., 314 (2006), 109–125 | MR | Zbl
[18] Csordas G., Williamson J., “The zeros of Jensen polynomials are simple”, Proc. Amer. Math. Soc., 49:1 (1975), 263–264 | MR | Zbl
[19] de Branges L., Hilbert Spaces of Entire Functions, Prentice Hall, Englewood Cliffs, N.J., 1968, ix+326 pp. | MR | Zbl
[20] Djrbashian M. M., Harmonic Analysis and Boundary Value Problems in the Complex Domain., Operator Theory Advances and Applications, 65, Birkhauser Verlag, Basel, Boston, Berlin, 1993, xiii+256 pp. | MR | Zbl
[21] Edrey A., Saff E., Varga R., Zeros of Sections of Power Series, Lect. Notes in Math, 1002, Springer-Verlag, Berlin, Heidelberg, New York, 1983, viii+115 pp. | MR
[22] Fenchel W., “Inégalités quadratiques entre des volumes mixtes des corps convexes”, C. R. Acad. Sci. Paris, 203, 647–650
[23] Fox C., “The asymptotic expansion of generalized hypergeometric functions”, Proc. Lond. Math. Soc., 27 (1928), 389–400 | DOI | Zbl
[24] Gantmacher F. R., The Theory of Matrices, Chelsea, New York, 1959, 1960 | MR
[25] Gasca M., Micchelli Ch. A. (eds), Total Positivity and its Applications, Kluver Academic Publishers, Dordrecht, Boston, London, 1996, x+518 pp. | MR
[26] Gray A., Tubes, $1^{th}$, Addison-Wesley, 1990 ; $2^{th}$, Birkhäuser Verlag, Basel, Boston, Berlin, 2005; Grei A., Trubki, $1^{th}$, Mir, Moskva, 1993 | MR | Zbl | MR
[27] Erdélyi A., Magnus W., Oberhettinger F., Tricomi F., Higher Transcendental Functions, v. III, McGraw-Hill, New York, Toronto, London, 1955, xvii+292 pp. ; Beitmen G., Erdeii A., Vysshie Transtsendentnye Funktsii, v. Tom III, Spravochnaya Matematicheskaya Biblioteka, Nauka, Moskva, 1967, 300 pp. | Zbl | MR
[28] Hadwiger H., Vorlesungen über Inhalt, Öberflache und Isoperimetrie, Springer, Berlin, Göttingen, Heidelberg, 1957, xiii+312 pp. (In German) ; Khadviger G., Lektsii ob ob'eme, ploschadi poverkhnosti i izoperimetrii, Nauka, Moskva, 1966, 416 pp. | MR
[29] Jensen J. L. W. V., “Recherches sur la théorie des équations”, Acta Mathem., 36 (1913), 181–195 | DOI | MR
[30] Karlin S., Total Positivity, Stanford Univ. Press, Stanford CA, 1968, xiv+576 pp. | MR
[31] Karlin S., Szegö G., “On certain determinants whose elements are orthogonal polynomials”, Journ. d'Analyse Mathem., 8 (1960), 1–157 | DOI | MR
[32] Klain D. A., Rota G.-C., Introduction to Geometric Probability, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl
[33] Krein M. G., Naimark M. A., “The Method of Symmetric and Hermitian Forms in the Theory of the Separation of the Roots of Algebraic Equations”, Linear and Multilinear Algebra, 10 (1981), 265–308 | DOI | MR | Zbl
[34] Kurtz D., “A sufficient condition for all the roots of a polynomial to be real”, Amer. Mathem. Monsley, 99:3 (1992), 259–263 | DOI | MR | Zbl
[35] Laguerre E., {ØE}UVRES, v. I, Second edition, Chelsea, New York, 1972, xx+468 pp. | MR
[36] Laguerre E., “Sur quelques points de la théorie des équations numéricues”, Acta Math., 4 (1884), 97–120 ; Reprinted in [Lag] 184–206 | DOI | MR
[37] Leichtweiß K., Konvexe Mengen. Convex sets, Springer, Berlin, 1980, 330 pp. (in German) ; Leikhtveis K., Vypuklye mnozhestva, Nauka, Moskva, 1985, 336 pp. | MR | Zbl | MR
[38] Levin B. Ja., Distribution of Zeros of Entire Functions, Transl. of Math. Monogr., 5, Revised Edition, Amer. Math. Soc., Providence, RI, 1980, xii+523 pp. | MR
[39] Levin B. Ja., Lectures on Entire Functions, Transl. of Mathem. Monogr., 150, Amer. Math. Soc., Providence, RI, 1996, xv+248 pp. | MR | Zbl
[40] Marden M., Geometry of Polynomials, 2nd edn., Amer. Math. Soc., Providence, R.I., 1966 | MR
[41] Minkowski H., Gesammelte Abhandlungen von Hermann Minkowski, Zweiter Band, Verlag von B. G. Teubner, Leipzig, Berlin, 1911, iv+466 pp.
[42] Minkowski H., “Theorie der konvexen Körper, insbesondere Begründung ihres Oberflächenbegriffs”, 131–229, in [Min]
[43] Minkowski H., “Volumen und Oberfläche”, Mathematische Annalen, 57, 447–495 | DOI | MR | Zbl
[44] Obreschkoff N., Verteilung und Berechnung der Nullstellen Reeller Polynomen, Deutscher Verlag der Wissenschaften, Berlin, 1963, viii+298 pp. | MR | Zbl
[45] Ostrovskii I. V., “On zero distribution of sections and tails of power series”, Israel Math. Conference Proc., 15 (2001), 297–310 | MR | Zbl
[46] Ostrovskii I., “On a problem of A. Eremenko”, Comput. Methods Func. Theory, 4:2 (2004), 275–282 | MR | Zbl
[47] Ostrovskii I. V., Peresyolkova I. N., “Nonasymptotic results on distribution of zeros of the function $E_\rho(z,\mu)$”, Analysis Mathematica, 23 (1997), 283–296 | DOI | MR | Zbl
[48] Pòlya G., Collected Papers, v. II, Location of Zeros, ed. R. P. Boas, MIT Press, Cambridge, MA, 1974, x+444 pp. | MR
[49] Pòlya G., “Über die Nullstellen gewisser ganzer Functionen [On zeros of certain entire functions]”, Math. Zeitschrift, 2 (1918), 352–383 (In German.) ; Reprinted in [Po] 166–197 | DOI | MR | Zbl
[50] Pòlya G., Schur I., “Über zwei arten von Faktorenfolgen in der Theorie der algebraischen Gleichungen”, Journ. für Reine Angew. Mathematik, 144 (1914), 89–113 ; Reprinted in [Po] 100–124 | Zbl
[51] Pòlya G., Szegö G., Aufgaben und Lehrsätze aus der Analysis, v. 2, Funktionentheorie. Nullstellen. Polynome. Determinanten. Zahlentheorie, Dritte Auflage, Springer-Verlag, Berlin, Göttingen, Heidelberg, New York, 1964 (In German) ; English translation: Pòlya G., Szegö G., Problems and Theorems in Analysis, v. II, Theory of functions, zeros, polynomials, determinants, number theory, geometry, Springer-Verlag, Berlin, 1998, xii+392 pp. ; Polia G., Sege G., Zadachi i Teoremy iz Analiza. Chast vtoraya. Teoriya funktsii. Raspredelenie nulei. Polinomy. Opredeliteli. Teoriya chisel, Trete izdanie, Nauka, Moskva, 1978, 432 pp. | Zbl | MR | MR
[52] Rahman Q. L. and G. Schmeisser, Analytic Theory of Polynomials, Clarendon Press, Oxford, 2002, xiv+742 pp. | MR | Zbl
[53] Schläfli L., Gesammelte Mathematische Abhandlungen, v. 1, Birkhäuser, Basel, 1950, 392 pp. | MR
[54] Schläfli L., “Theorie der vielfachen Kontinuität”, 167–387, in [Schl]
[55] Schneider R., Convex Bodies: The Brunn-Minkowski Theory, Cambridge Univ. Press, Cambridge, 1993 | MR
[56] Schur I., Gesammelte Abhandlungen [Collected Works], v. II, Springer-Verlag, Berlin, Heidelberg, New York, 1973
[57] Schur I., “Zwei Sätze über algebraische Gleichungen mit lauter reelen Wurzeln [Two theorems on algebraic equations with only real roots]”, Journal für reine und angew. Mathem., 144 (1914), 75–88 (In German) ; Reprinted in: [Schu] 56–69 | DOI | Zbl
[58] Shephard G., “Inequalities between mixed volumes of convex sets”, Mathematika, 7:2 (1960), 125–138 | DOI | MR | Zbl
[59] Shail-Small, Complex Polynomials, Cambridge Univ. Press, Cambridge, 2002 | MR
[60] Steiner J., Jacob Steiner's Gesammelte Werke (K. Weierstrass-Herausgeg), v. 2, Verlag von G. Reimer, Berlin, 1882
[61] Szegö G., Collected Papers 1915–1927, v. 1, eds. Askey R., Birkhäuser, Boston, Basel, Stuttgart, 1982 | MR | Zbl
[62] Szegö G., “Über eine Eigenschaft der Exponentialreihe”, Sitzungsbericht. Berlin. Math. Gesellsch., 23 (1924), 50–64 ; Reprinted in [Sz] 646–660 | Zbl
[63] Steiner J., “Über parallele Flächen”, Monatsbericht der Akademie der Wissenschaften zu Berlin, 1840, 114–118; Reprinted in [St] 172–176
[64] Titchmarsh E. C., The Theory Of Functions, Oxford University Press, Oxford
[65] A Treatise on the Theory of Bessel Functions, Second ed., Cambridge Univ. Press, Cambridge, 1944 | MR
[66] Watson G. N., “A class of integral functions defined by Taylor's series”, Trans. Cambr. Philoc. Soc., 22 (1913), 15–37 | Zbl
[67] Webster R., Convexity, Oxford University Press, Oxford, New York, Tokyo, 1994, xviii+444 pp. | MR | Zbl
[68] Weyl H., Gesammelte Abhandlungen, v. III, eds. Chandrasekharan, Springer-Verlag, Berlin, Heidelberg, New York, 1968 | MR | Zbl
[69] Weyl H., Selected Papers, eds. Arnold V.I., Parshin A. N., Nauka, Moskow, 1984, 512 pp. | MR | Zbl
[70] Weyl H., “On the volume of tubes”, Amer. Journ of Math., 61 (1939), 461–472 ; Reprinted in [Wey] 658–670; Veil G., “Ob ob'eme trub”, 246–255, v [WeyR] | DOI | MR
[71] Whittakwer E. T., Watson G. N., A Course of Modern Analysis, Cambridge Univ. Press, Cambridge, 1927, vi+608 pp. ; Uitteker E. T., Vatson Dzh. N., Kurs Sovremennogo Analiza, v. 2, Fizmatgiz, Moskva, 1963, 515 pp. | MR
[72] Wright E. M., “The asymptotic expansion of the generalized hypergeometric functions”, Journ. London Math., 10 (1935), 286–293 | DOI
[73] Wright E. M., “The asymptotic expansion of integral functions defined by Tailor series”, Philosoph. Trans. Royal Soc. London A, 238:795 (1940), 423–451 | DOI | MR