On the Growth of Universal Meromorphic Functions

Luh, Wolfgang; Martirosian, Valeri A.

doi:10.1524/anly.2000.20.2.137

Search citation statements

Order By: Relevance

Paper Sections

Select...

Lemma1

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2005

2018

Publication Types

Select...

Article4

Relationship

Self Cite0

Independent4

Authors

Journals

Cited by 4 publications

(3 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In view of (40), we see that these modifications of (21) and (22) imply that inequality (23) and the inequality immediately following it hold without alteration in the case n = 2. The proof of Lemma 4 for n = 2 can now be completed exactly as in the final sentence of Section 2.4.…”

Section: Lemmamentioning

confidence: 94%

See 2 more Smart Citations

Permissible growth rates for Birkhoff type universal harmonic functions

Armitage

2005

Journal of Approximation Theory

View full text Add to dashboard Cite

A harmonic function H on R n (n 2) is said to be universal (in the sense of Birkhoff) if its set of translates {x → H (a + x): a ∈ R n } is dense in the space of all harmonic functions on R n with the topology of local uniform convergence. The main theorem includes the result that such functions, H, can have any prescribed order and type. The growth result is compared with a similar known theorem for G.D. Birkhoff's universal holomorphic functions and contrasted with known growth theorems for MacLane-type universal harmonic and holomorphic functions.

show abstract

Section: Lemmamentioning

confidence: 94%

“…Hence ∞ 1 H m converges locally uniformly on R n to some harmonic function H on R n . It follows from (24) …”

Section: 2mentioning

confidence: 99%