Normal families of meromorphic functions with multiple zeros and poles

Xuecheng Pang; Lawrence Zalcman

doi:10.1007/bf02807190

Normal families of meromorphic functions with multiple zeros and poles

Xuecheng Pang
, Lawrence Zalcman

Department of Mathematics

East China Normal University

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

Let F be a family of functions meromorphic in the plane domain D, all of whose zeros and poles are multiple. Let h be a continuous function on D. Suppose that, for each f ∈ F, f′ (z) ≠ h(z) for z ∈ D. We show that if h(z) ≠ 0 for all z ∈ D, or if h is holomorphic on D but not identically zero there and all zeros of functions in F have multiplicity at least 3, then F is a normal family on D.

Original language	English
Pages (from-to)	1-9
Number of pages	9
Journal	Israel Journal of Mathematics
Volume	136
DOIs	https://doi.org/10.1007/bf02807190
State	Published - 2003

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: [email protected] (X. Huang), [email protected] (Y. Gu). 1 The second author’s research is supported by NNSF of China No. 19971097.

Funding

* Corresponding author. E-mail addresses: [email protected] (X. Huang), [email protected] (Y. Gu). 1 The second author’s research is supported by NNSF of China No. 19971097.

Funders	Funder number
National Natural Science Foundation of China	19971097

Access to Document

10.1007/bf02807190

Cite this

@article{aab03b2c8e8a4854836000d55203b0b4,

title = "Normal families of meromorphic functions with multiple zeros and poles",

abstract = "Let F be a family of functions meromorphic in the plane domain D, all of whose zeros and poles are multiple. Let h be a continuous function on D. Suppose that, for each f ∈ F, f′ (z) ≠ h(z) for z ∈ D. We show that if h(z) ≠ 0 for all z ∈ D, or if h is holomorphic on D but not identically zero there and all zeros of functions in F have multiplicity at least 3, then F is a normal family on D.",

author = "Xuecheng Pang and Lawrence Zalcman",

note = "Funding Information: * Corresponding author. E-mail addresses: hx\[email protected] (X. Huang), [email protected] (Y. Gu). 1 The second author{\textquoteright}s research is supported by NNSF of China No. 19971097.",

year = "2003",

doi = "10.1007/bf02807190",

language = "אנגלית",

volume = "136",

pages = "1--9",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

}

TY - JOUR

T1 - Normal families of meromorphic functions with multiple zeros and poles

AU - Pang, Xuecheng

AU - Zalcman, Lawrence

N1 - Funding Information: * Corresponding author. E-mail addresses: [email protected] (X. Huang), [email protected] (Y. Gu). 1 The second author’s research is supported by NNSF of China No. 19971097.

PY - 2003

Y1 - 2003

N2 - Let F be a family of functions meromorphic in the plane domain D, all of whose zeros and poles are multiple. Let h be a continuous function on D. Suppose that, for each f ∈ F, f′ (z) ≠ h(z) for z ∈ D. We show that if h(z) ≠ 0 for all z ∈ D, or if h is holomorphic on D but not identically zero there and all zeros of functions in F have multiplicity at least 3, then F is a normal family on D.

AB - Let F be a family of functions meromorphic in the plane domain D, all of whose zeros and poles are multiple. Let h be a continuous function on D. Suppose that, for each f ∈ F, f′ (z) ≠ h(z) for z ∈ D. We show that if h(z) ≠ 0 for all z ∈ D, or if h is holomorphic on D but not identically zero there and all zeros of functions in F have multiplicity at least 3, then F is a normal family on D.

UR - https://www.scopus.com/pages/publications/0141725726

U2 - 10.1007/bf02807190

DO - 10.1007/bf02807190

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0141725726

SN - 0021-2172

VL - 136

SP - 1

EP - 9

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

Normal families of meromorphic functions with multiple zeros and poles

Abstract

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this