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Journal articles on the topic 'Normal functions'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

Xu, Yan. "Normal functions and α-Normal Functions." Acta Mathematica Sinica 16, no. 3 (July 2000): 399–404. http://dx.doi.org/10.1007/s101140000041.

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2

Xu, Yan. "Normal functions and α-Normal Functions." Acta Mathematica Sinica, English Series 16, no. 3 (July 2000): 399–404. http://dx.doi.org/10.1007/pl00011551.

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3

Kojecký, Tomáš. "Some functions of eigenvalues of normal operator." Applications of Mathematics 35, no. 5 (1990): 356–60. http://dx.doi.org/10.21136/am.1990.104417.

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4

Riihentaus, Juhani. "Removable singularities for Bloch and normal functions." Czechoslovak Mathematical Journal 43, no. 4 (1993): 723–41. http://dx.doi.org/10.21136/cmj.1993.128430.

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5

Kayathri, K., O. Ravi, M. L. Thivagar, and M. Joseph Israel. "Mildly ($1,2)^*$-normal spaces and some bitopological functions." Mathematica Bohemica 135, no. 1 (2010): 1–13. http://dx.doi.org/10.21136/mb.2010.140676.

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6

Charpin, Pascale. "Normal Boolean functions." Journal of Complexity 20, no. 2-3 (April 2004): 245–65. http://dx.doi.org/10.1016/j.jco.2003.08.010.

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7

Makhmutov, Shamil. "α-normal functions and yosida functions." Complex Variables, Theory and Application: An International Journal 43, no. 3-4 (February 2001): 351–62. http://dx.doi.org/10.1080/17476930108815325.

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8

Pengcheng, Wu. "On increasing functions, bloch functions and normal functions." Complex Variables, Theory and Application: An International Journal 35, no. 2 (March 1998): 157–70. http://dx.doi.org/10.1080/17476939808815078.

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9

Reid, J. G. "Normal functions of normal random variables." Computers & Mathematics with Applications 14, no. 3 (1987): 157–60. http://dx.doi.org/10.1016/0898-1221(87)90147-7.

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10

Hwang, J. S., and Peter Lappan. "Coefficients of Bloch functions and normal functions." Annales Academiae Scientiarum Fennicae Series A I Mathematica 12 (1987): 69–75. http://dx.doi.org/10.5186/aasfm.1987.1214.

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11

Chen, Huaihui, and Paul M. Gauthier. "On Strongly Normal Functions." Canadian Mathematical Bulletin 39, no. 4 (December 1, 1996): 408–19. http://dx.doi.org/10.4153/cmb-1996-049-4.

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AbstractLoosely speaking, a function (meromorphic or harmonic) from the hyperbolic disk of the complex plane to the Riemann sphere is normal if its dilatation is bounded. We call a function strongly normal if its dilatation vanishes at the boundary. A sequential property of this class of functions is proved. Certain integral conditions, known to be sufficient for normality, are shown to be in fact sufficient for strong normality.

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12

Xu, Yan. "The α-normal functions." Computers & Mathematics with Applications 44, no. 3-4 (August 2002): 357–63. http://dx.doi.org/10.1016/s0898-1221(02)00154-2.

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13

Chen, Huaihui, and Paul M. Gauthier. "Normal Functions: Lp Estimates." Canadian Journal of Mathematics 49, no. 1 (February 1, 1997): 55–73. http://dx.doi.org/10.4153/cjm-1997-003-6.

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AbstractFor ameromorphic (or harmonic) function ƒ, let us call the dilation of ƒ at z the ratio of the (spherical)metric at ƒ(z) and the (hyperbolic)metric at z. Inequalities are knownwhich estimate the sup norm of the dilation in terms of its Lp norm, for p > 2, while capitalizing on the symmetries of ƒ. In the present paper we weaken the hypothesis by showing that such estimates persist even if the Lp norms are taken only over the set of z on which ƒ takes values in a fixed spherical disk. Naturally, the bigger the disk, the better the estimate. Also, We give estimates for holomorphic functions without zeros and for harmonic functions in the case that p = 2.

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14

Harding, John, Carol Walker, and Elbert Walker. "Convex normal functions revisited." Fuzzy Sets and Systems 161, no. 9 (May 2010): 1343–49. http://dx.doi.org/10.1016/j.fss.2008.10.008.

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15

Niu, P., and Y. Xu. "Normal families of meromorphic functions and shared functions." Journal of Contemporary Mathematical Analysis 51, no. 3 (May 2016): 160–65. http://dx.doi.org/10.3103/s1068362316030067.

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16

Gauthier, P. M., and J. Xiao. "Functions of bounded expansion: normal and Bloch functions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 66, no. 2 (April 1999): 168–88. http://dx.doi.org/10.1017/s144678870003929x.

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AbstractNormal functions and Bloch functions are respectively functions of bounded spherical expansion and bounded Euclidean expansion. In this paper we discuss the behaviour of normal functions and of Bloch functions in terms of the maximal ideal space of H∞, the Bergman projection and the Ahlfors-Shimizu characteristic.

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17

Dovbush, P. V. "Boundary behaviour of Bloch functions and normal functions." Complex Variables and Elliptic Equations 55, no. 1-3 (June 12, 2009): 157–66. http://dx.doi.org/10.1080/17476930902999108.

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18

Wu, Pengcheng. "Increasing functions, harmonic bloch and harmonic normal functions." Complex Variables, Theory and Application: An International Journal 40, no. 2 (December 1999): 133–37. http://dx.doi.org/10.1080/17476939908815212.

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19

Chen, Jun-Fan, and Ming-Liang Fang. "Normal families and shared functions of meromorphic functions." Israel Journal of Mathematics 180, no. 1 (October 31, 2010): 129–42. http://dx.doi.org/10.1007/s11856-010-0097-7.

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20

Girela, Daniel, and Daniel Suárez. "On Blaschke products, Bloch functions and normal functions." Revista Matemática Complutense 24, no. 1 (February 5, 2010): 49–57. http://dx.doi.org/10.1007/s13163-010-0027-6.

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21

Cheng-Xiong, Sun. "Normal families of meromorphic functions concerning shared functions." Kragujevac Journal of Mathematics 39, no. 2 (2015): 149–54. http://dx.doi.org/10.5937/kgjmath1502149c.

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22

Aulaskari, Rauno, and Ruhan Zhao. "Some Characterizations of Normal and Little Normal Functions." Complex Variables, Theory and Application: An International Journal 28, no. 2 (October 1995): 135–48. http://dx.doi.org/10.1080/17476939508814843.

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23

Wulan, Hasi. "Some problems on normal and little normal functions." Complex Variables, Theory and Application: An International Journal 36, no. 3 (November 1998): 301–9. http://dx.doi.org/10.1080/17476939808815115.

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24

Berberyan, S. L. "Boundedness of normal harmonic functions." Moscow University Mathematics Bulletin 68, no. 2 (March 2013): 122–25. http://dx.doi.org/10.3103/s0027132213020101.

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25

Proskurnin, I. A. "Normal Forms of Equivariant Functions." Moscow University Mathematics Bulletin 75, no. 2 (March 2020): 83–86. http://dx.doi.org/10.3103/s0027132220020072.

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26

Wang, Jian-Ping. "NORMAL FAMILY OF MEROMORPHIC FUNCTIONS." Bulletin of the Korean Mathematical Society 51, no. 3 (May 31, 2014): 691–700. http://dx.doi.org/10.4134/bkms.2014.51.3.691.

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27

McFarland, Lynne V. "Normal flora: diversity and functions." Microbial Ecology in Health and Disease 12, no. 4 (January 2000): 193–207. http://dx.doi.org/10.1080/08910600050216183.

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28

Sun, Cheng Xiong. "Normal Families and Shared Functions." Fasciculi Mathematici 60, no. 1 (June 1, 2018): 173–80. http://dx.doi.org/10.1515/fascmath-2018-0011.

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Abstract Let k ∈ ℕ, m ∈ℕ ∪{0}, and let a(z)(≢ 0) be a holomorphic function, all zeros of a(z) have multiplicities at most m. Let ℱ be a family of meromorphic functions in D. If for each f ∈ℱ, the zeros of f have multiplicities at least k + m + 1 and all poles of f are of multiplicity at least m + 1, and for f,g ∈ℱ, ff(k)−a(z) and gg(k)−a(z) share 0, then ℱ is normal in D. Some examples are given to show that the conditions are best, and the result removes the condition “m is an even integer” in the result due to Sun [Kragujevac Journal of Math 38(2), 173-282, 2014].

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29

Clemens, C. Herbert. "Intersection numbers for normal functions." Journal of Algebraic Geometry 22, no. 3 (December 19, 2012): 565–73. http://dx.doi.org/10.1090/s1056-3911-2012-00582-7.

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30

Chen, Huai-Hui, and Xin-Hou Hua. "Normal families of holomorphic functions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 59, no. 1 (August 1995): 112–17. http://dx.doi.org/10.1017/s1446788700038490.

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AbstractLet a(z) be a meromorphic function with only simple poles, and let k∈ N. Suppose that f(z) is meromorphic. We first set up an inequality in which T(r, f) is bounded by the counting function of the zeros of f(k) + af2, and then we prove a corresponding normal criterion. An example shows that the restriction on the poles of a(z) is best possible.

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31

张, 莎莎. "Normal Families Concerning Exceptional Functions." Pure Mathematics 04, no. 04 (2014): 117–21. http://dx.doi.org/10.12677/pm.2014.44018.

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32

Chang, Jianming, Mingliang Fang, and Lawrence Zalcman. "Normal families of holomorphic functions." Illinois Journal of Mathematics 48, no. 1 (January 2004): 319–37. http://dx.doi.org/10.1215/ijm/1258136186.

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33

Xu, Yan, and Huiling Qiu. "Normal functions and shared sets." Filomat 30, no. 2 (2016): 287–92. http://dx.doi.org/10.2298/fil1602287x.

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34

Carlet, C., H. Dobbertin, and G. Leander. "Normal Extensions of Bent Functions." IEEE Transactions on Information Theory 50, no. 11 (November 2004): 2880–85. http://dx.doi.org/10.1109/tit.2004.836681.

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35

Morrison, David R., and Johannes Walcher. "D-branes and normal functions." Advances in Theoretical and Mathematical Physics 13, no. 2 (2009): 553–98. http://dx.doi.org/10.4310/atmp.2009.v13.n2.a5.

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36

Pang, Xuecheng, Degui Yang, and Lawrence Zalcman. "Normal families and omitted functions." Indiana University Mathematics Journal 54, no. 1 (2005): 223–36. http://dx.doi.org/10.1512/iumj.2005.54.2492.

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37

Zamarashkin, N. L., E. E. Tyrtyshnikov, and V. N. Chugunov. "Functions generating normal Toeplitz matrices." Mathematical Notes 89, no. 3-4 (April 2011): 480–83. http://dx.doi.org/10.1134/s0001434611030199.

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38

Brosnan, Patrick, Hao Fang, Zhaohu Nie, and Gregory Pearlstein. "Singularities of admissible normal functions." Inventiones mathematicae 177, no. 3 (April 16, 2009): 599–629. http://dx.doi.org/10.1007/s00222-009-0191-9.

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39

Harding, John, Carol Walker, and Elbert Walker. "Lattices of convex normal functions." Fuzzy Sets and Systems 159, no. 9 (May 2008): 1061–71. http://dx.doi.org/10.1016/j.fss.2007.09.009.

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40

Xiaojun, Huang, and Gu Yongxing. "Normal Families of Meromorphic Functions." Results in Mathematics 49, no. 3-4 (December 2006): 279–88. http://dx.doi.org/10.1007/s00025-006-0224-2.

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41

Sun, Daochun, and Le Yang. "Normal family of algebroidal functions." Science in China Series A: Mathematics 44, no. 10 (October 2001): 1271–77. http://dx.doi.org/10.1007/bf02877015.

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42

Aleksandrov, Aleksei, Vladimir Peller, Denis Potapov, and Fedor Sukochev. "Functions of perturbed normal operators." Comptes Rendus Mathematique 348, no. 9-10 (May 2010): 553–58. http://dx.doi.org/10.1016/j.crma.2010.04.015.

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43

Xu, Yan. "Normal families and exceptional functions." Journal of Mathematical Analysis and Applications 329, no. 2 (May 2007): 1343–54. http://dx.doi.org/10.1016/j.jmaa.2006.07.021.

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44

Chen, Wei, Yingying Zhang, Jiwen Zeng, and Honggen Tian. "Normal Criterion Concerning Shared Values." Journal of Applied Mathematics 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/312324.

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We study normal criterion of meromorphic functions shared values, we obtain the following. LetFbe a family of meromorphic functions in a domainD, such that functionf∈Fhas zeros of multiplicity at least 2, there exists nonzero complex numbersbf,cfdepending onfsatisfying(i) bf/cfis a constant; (ii)min {σ(0,bf),σ(0,cf),σ(bf,cf)≥m}for somem>0; (iii) (1/cfk-1)(f′)k(z)+f(z)≠bfk/cfk-1or(1/cfk-1)(f′)k(z)+f(z)=bfk/cfk-1⇒f(z)=bf, thenFis normal. These results improve some earlier previous results.

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45

Xiao, Jie. "Some properties and characterizations ofA-normal functions." International Journal of Mathematics and Mathematical Sciences 20, no. 3 (1997): 503–10. http://dx.doi.org/10.1155/s0161171297000689.

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LetMbe the set of all functions meromorphic onD={z∈ℂ:|z|<1}. Fora∈(0,1], a functionf∈Mis calleda-normal function of bounded (vanishing) type orf∈Na(N0a), ifsupz∈D(1−|z|)af#(z)<∞(lim|z|→1(1−|z|)af#(z)=0). In this paper we not only show the discontinuity ofNaandN0arelative to containment asavaries, which shows∪0<a<1Na⊂UBC0, but also give several characterizations ofNaandN0awhich are real extensions for characterizations ofNandN0.

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46

Chen, Jun-Fan. "Nonexceptional functions and normal families of zero-free meromorphic functions." Filomat 31, no. 14 (2017): 4665–71. http://dx.doi.org/10.2298/fil1714665c.

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Let k be a positive integer, let F be a family of zero-free meromorphic functions in a domain D, all of whose poles are multiple, and let h be a meromorphic function in D, all of whose poles are simple, h . 0, ?. If for each f ? F, f(k)(z)- h(z) has at most k zeros in D, ignoring multiplicities, then F is normal in D. The examples are provided to show that the result is sharp.

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47

Favorov, S. Ju. "Sunyer-i-Balaguer’s almost elliptic functions and Yosida’s normal functions." Journal d'Analyse Mathématique 104, no. 1 (January 2008): 307–40. http://dx.doi.org/10.1007/s11854-008-0026-4.

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48

Fish, Alexander. "Random Liouville functions and normal sets." Acta Arithmetica 120, no. 2 (2005): 191–96. http://dx.doi.org/10.4064/aa120-2-6.

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49

Calso, Cristina, Jérémy Besnard, and Philippe Allain. "Normal aging of frontal lobe functions." Gériatrie et Psychologie Neuropsychiatrie du Viellissement 14, no. 1 (March 2016): 77–85. http://dx.doi.org/10.1684/pnv.2016.0586.

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50

Lu, Feng. "NORMAL FAMILIES AND SHARED HOLOMORPHIC FUNCTIONS." Bulletin of the Korean Mathematical Society 49, no. 1 (January 31, 2012): 197–204. http://dx.doi.org/10.4134/bkms.2012.49.1.197.

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