ISSN:0278-1077    

DOI:10.1080/17476939708815032

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

Let, be a linear differential operator, whose coefficients are (constants or) 2φi-periodic entire functions of order one, mean type. We will prove that any exceptional solution ofL[L] = 0, i.e., any solution satisfying, has the formwhereq≥ 1 is an integer, thecj's are complex constants andSand thePj's are polynomials. We give also a new proof of a result due to Steinbart, who classified the so-called subnormal solutions-solutions satisfying.

ISSN:0278-1077    

DOI:10.1080/17476939708815033

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In an earlier paper of the author's, existence of a complete formal solution for non-linear systems has been shown. Here, we investigate their multi-summability properties.

ISSN:0278-1077    

DOI:10.1080/17476939708815034

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

We prove that the periodic equationadmits a solution with finite exponent of convergence if and only ifwherenis a non-negative integer satisfying a certain (n+ 1) × (n+ 1)-determinant condition. Moreover, we obtain explicit representations for such solutions. Our result is somewhat similar to a result due to Bank, Laine and Langley [5] for a second order equation.

ISSN:0278-1077    

DOI:10.1080/17476939708815035

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

It is well known that for meromorphic functions that share values (ignoring multiplicities), the “dividing line” between the trivial case and the nontrivial examples occurs between four and five shared values. In this paper we show that for meromorphic functions that share pairs of values (ignoring multiplicities), the “dividing line” between the trivial case and the nontrivial examples occurs between five and six pairs of values. We also discuss meromorphic functions that share four pairs of values.

ISSN:0278-1077    

DOI:10.1080/17476939708815036

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In this paper, we discuss the relation between BMOA (or Hardy-Orlicz Space HBa) and areally meanp-valent functionsA(p), some growth estimates of f'/ff(n)forfεA(p) are given; we find also some relations betweenA(p) and the class of normalization univalent functionsS; Finally, we obtain a quantitative estimate on integral means of |f′|λforfεA(p) and λ>(2/(4p+1)).

ISSN:0278-1077    

DOI:10.1080/17476939708815037

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

Suppose thatgis a transcendental entire function andfis transcendental and meromorphic in the plane, such that the composition F=fˆg has finite order, whileQis a rational function. We prove thatF−Qcannot have sum of deficiencies 2. The result is related to a theorem of Goldstein and to results on the frequency of fixpoints of compositions of functions.

ISSN:0278-1077    

DOI:10.1080/17476939708815038

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

Letfbe a meromorphic function in the plane, denote by A(r,f) the spherical area off({z:|z|≤r}) divided by the area of the Riemann sphere. For aa∈CputandPutB(f) = {a:b(a,f)<0}. Then the setB(f) is at most countable for every meromorphic functionf. If there existsa0such thatb(a0f)<2π thenB(f)={a0}. OtherwiseFor functionsfof order λ>1/2 we always have (1) and more, for any set {a1,…,aq} ⊂ Ȼ there is a sequencerk→∞ such that.

ISSN:0278-1077    

DOI:10.1080/17476939708815039

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

We use a modification of an inequality of the first author on the means of Green's functions to prove thelongest arcconjecture for δ-subharmonic functions.

ISSN:0278-1077    

DOI:10.1080/17476939708815040

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In this paper, we prove that the solutions with infinite exponent of convergence of zeros for higher order homogeneous linear differential equations with one dominant coefficient must exist, and discuss the growth of these solutions.

ISSN:0278-1077    

DOI:10.1080/17476939708815041

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor