Some results on the fix-points and factorization of entire and meromorphic functions
ジャーナル
フリー
1976 年 28 巻 1 号 p. 144-159
詳細
- Published: 1976 Received: 1975/04/08 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
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訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報 訂正内容: Wrong : 1) I. N. Baker, Permutable power series and regular iteration, J. Austral. Math. Soc., 2 (1962), 265-294.
2) I. N. Baker, Fix-points and iterates of entire functions, Math. Z., 71 (1959), 146-153.
3) I. N. Baker, Fix-points of polynomials and rational functions, J. of London Math. Soc., 39 (1964), 615-622.
4) I. N. Baker and F. Gross, Further results on factorization of entire functions, Proc. of Symp. in Pure and Applied Math., Vol. II; Entire functions and related parts of Analysis, 1968, 30-35.
5) E. Borel, Sur les zeros des fonctions entières, Acta Math., 20 (1897).
6) H. Brolin, Invariant sets under iteration of rational functions, Ark. Mat., Bd. 6, Nr. 6 (1965), 103-144.
7) H. Cremer, Über die iteration rationales funktionen, Jber. Deutsch. Math. Verein., 33 (1925), 185-210.
8) H. Cremer, Über die Schrödersche funktional gleichung und das Schwarzsehe Eckenabbildungs-problem, Ber. Math.-Phys. Klasse der Sächs, Akad. Leipzig, Setjung Vom 13, Juni 1932. 84, (1932), 291-324.
9) A. Edrei and W.H.J. Fuchs, Valeurs déficientes et valeurs asymptotiques des fonctions méromorphes, Comment. Math. Helv., 33 (1959), f. 4, 258-295.
10) P. Fatou, Sur l'itération des fonctions transcendants entieres, Acta Math., 47 (1926).
11) F. Gross, On factorization of meromorphic functions, Trans. Amer. Math. Soc., 131, No. 1, April (1968), 215-222.
12) F. Gross, Prime entire functions, Trans. Amer. Math. Soc., 161 (1971), 219-233.
13) F. Gross, Factorization of entire functions which are periodic mod g, Indian J. Pure Appl. Math., 2 (1971).
14) F. Gross and C.C. Yang, The fix-points and factorization on meromorphic functions, Trans. Amer. Math. Soc., 168 (1972), 211-219.
15) F. Gross and C.C. Yang, On factorization of entire functions with infinitely many real zeros, Indian J. Pure Appl. Math., 3, No. 6, (1972).
16) R. Goldstein, On factorization of certain entire functions, J. London Math. Soc. (2), 2 (1970), 221-224.
17) W. K. Hayman, Meromorphic functions, Oxford, 1964.
18) W. K. Hayman, Picard values of meromorphic functions and their derivatives, Ann, of Math., 70 (1959), 9-42.
19) G. Julia, Mémoire sur l'itération des fonctions rationelles, J. Math. Pures et Appl., (8), 1 (1918), 47-245.
20) M. Kuczma, Functional Equations, Polska Akademia Nauk Mongrafie Matematyczne, Warszawa, Poland, 1968.
21) J. Myrberg, Iteration der polynome mit reelen koeffizienten, Ann. Acad. Sci. Fenn. Ser., AI., 374 (1965).
22) R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris, 1929, 61-63.
23) M. Ozawa, On prime entire functions, Pt. 1: Kodai Math. Sem. Rep., 22 (1970), 301-308; Pt. II: Kodai Math. Sem. Rep., 22 (1970), 309-312.
24) G. Pólya, On an integral function of an integral function, J. London Math. Soc., 1 (1926), 12-15.
25) P. C. Rosenbloom, The fix-points of entire functions, Medd. Lunds Univ. Mat. Sem., Tome Suppl. (1952), 186-192.
26) P. C. Rosenbloom, L'itération des fonctions entières, C. R. Acad. Sci., Paris, 227 (1948), 382-383.
27) H. Töpfer, Über die iteration der ganzen transzendenten funktionen insbesondere von sin and cos, Math. Ann., 119 (1940), 65-84.
28) A. Wiman, Sur une extension d'un théorème de M. Hadamard, Arkiv Math. Astr. Och. Fys. 2, No. 14 (1905), 5.
29) C. C. Yang, On the dependence of the zeros of an entire function and its factorization, J. of Math. Anal. Appl., 35, 2 (1971), 374-380.
30) C. C. Yang, On deficiencies of differential polynomials, Math. Z., 116 (1970).
Right : [1] I. N. Baker, Permutable power series and regular iteration, J. Austral. Math. Soc., 2 (1962), 265-294.
[2] I. N. Baker, Fix-points and iterates of entire functions, Math. Z., 71 (1959), 146-153.
[3] I. N. Baker, Fix-points of polynomials and rational functions, J. of London Math. Soc., 39 (1964), 615-622.
[4] I. N. Baker and F. Gross, Further results on factorization of entire functions, Proc. of Symp. in Pure and Applied Math., Vol. II; Entire functions and related parts of Analysis, 1968, 30-35.
[5] E. Borel, Sur les zeros des fonctions entières, Acta Math., 20 (1897).
[6] H. Brolin, Invariant sets under iteration of rational functions, Ark. Mat., Bd. 6, Nr. 6 (1965), 103-144.
[7] H. Cremer, Über die iteration rationales funktionen, Jber. Deutsch. Math. Verein., 33 (1925), 185-210.
[8] H. Cremer, Über die Schrödersche funktional gleichung und das Schwarzsehe Eckenabbildungs-problem, Ber. Math. -Phys. Klasse der Sächs, Akad. Leipzig, Setjung Vom 13, Juni 1932. 84, (1932), 291-324.
[9] A. Edrei and W. H. J. Fuchs, Valeurs déficientes et valeurs asymptotiques des fonctions méromorphes, Comment. Math. Helv., 33 (1959), f. 4, 258-295.
[10] P. Fatou, Sur l'itération des fonctions transcendants entières, Acta Math., 47 (1926).
[11] F. Gross, On factorization of meromorphic functions, Trans. Amer. Math. Soc., 131, No. 1, April (1968), 215-222.
[12] F. Gross, Prime entire functions, Trans. Amer. Math. Soc., 161 (1971), 219-233.
[13] F. Gross, Factorization of entire functions which are periodic mod g, Indian J. Pure Appl. Math., 2 (1971).
[14] F. Gross and C.C. Yang, The fix-points and factorization on meromorphic functions, Trans. Amer. Math. Soc., 168 (1972), 211-219.
[15] F. Gross and C.C. Yang, On factorization of entire functions with infinitely many real zeros, Indian J. Pure Appl. Math., 3, No. 6, (1972).
[16] R. Goldstein, On factorization of certain entire functions, J. London Math. Soc. (2), 2 (1970), 221-224.
[17] W. K. Hayman, Meromorphic functions, Oxford, 1964.
[18] W. K. Hayman, Picard values of meromorphic functions and their derivatives, Ann, of Math., 70 (1959), 9-42.
[19] G. Julia, Mémoire sur l'itération des fonctions rationelles, J. Math. Pures et Appl., (8), 1 (1918), 47-245.
[20] M. Kuczma, Functional Equations, Polska Akademia Nauk Mongrafie Matematyczne, Warszawa, Poland, 1968.
[21] J. Myrberg, Iteration der polynome mit reelen koeffizienten, Ann. Acad. Sci. Fenn. Ser., AI., 374 (1965).
[22] R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris, 1929, 61-63.
[23] M. Ozawa, On prime entire functions, Pt. 1: Kodai Math. Sem. Rep., 22 (1970), 301-308; Pt. II: Kodai Math. Sem. Rep., 22 (1970), 309-312.
[24] G. Pólya, On an integral function of an integral function, J. London Math. Soc., 1 (1926), 12-15.
[25] P. C. Rosenbloom, The fix-points of entire functions, Medd. Lunds Univ. Mat. Sem., Tome Suppl. (1952), 186-192.
[26] P. C. Rosenbloom, L'itération des fonctions entières, C. R. Acad. Sci., Paris, 227 (1948), 382-383.
[27] H. Töpfer, Über die iteration der ganzen transzendenten funktionen insbesondere von sin and cos, Math. Ann., 119 (1940), 65-84.
[28] A. Wiman, Sur une extension d'un théorème de M. Hadamard, Arkiv Math. Astr. Och. Fys. 2, No. 14 (1905), 5.
[29] C. C. Yang, On the dependence of the zeros of an entire function and its factorization, J. of Math. Anal. Appl., 35, 2 (1971), 374-380.
[30] C. C. Yang, On deficiencies of differential polynomials, Math. Z., 116 (1970).
訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル 訂正内容: -
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