摘要:

An estimate for theLlogLnorm of the conjugate function operator is derived, for functions in classLlog logL.

ISSN:0278-1077    

DOI:10.1080/17476939808815131

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

We show that there exists a setSwith 11 elements such that the conditionEf(S)=Eg(S) impliesf=ffor any pair of non-constant meromorphic functionsfandg. For the prwf we generalise an estimate of Yi and Mues/Reinders on meromorphic functions sharing one value.

ISSN:0278-1077    

DOI:10.1080/17476939808815132

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

Letf(z)be an entire function of finite lower order λ and representable by a gap power serieswhere A ⊂ N and. In the paper we prove that if γ is an unbounded curve which meets every circle [∣,z∣, = r] once and λΔ < 1/3 then the inequalityis valid.

ISSN:0278-1077    

DOI:10.1080/17476939808815133

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

An inquality of the first author involving circular means of classical Green's functions is extended to fine Green's functions on fine domains. The inequality leads to a more natural proof of the longest arc relation recently proved by the authors.

ISSN:0278-1077    

DOI:10.1080/17476939808815134

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939808815135

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939808815136

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

This paper exhibits several results and conjectures of second main theorem type. Pani-cularly, it shows that the defect bound 2nfor holomorphic mappingsand nonlinear divisors without any nondegeneracy conditions proved by Shiffman. Eremenko and Sodin can be replaced byn+1 for certain mappingsfand some nonlinear divisors, for example, Fermat divisors, under the condition of algebraic nondegeneracy onf. For the case of linear divisors, the result coincides with Ru-Stoll's theorem and our proof can be viewed as a notes of their proof in the case of nonlinear divisors.

ISSN:0278-1077    

DOI:10.1080/17476939808815137

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

Suppose thatf(z) =g(z)/znwheregis a real entire function of finite order withg(0)≠ 0 andnis a positive integer, and thatff′, andf″ have only red zeros. We prove thatthengis a polynomial of degree not exceedingn+1. This strengthens an earlier result of the author, when one had to consider derivatives up to an order depending onfand the order of the entire functiongConversely, iffis of this form wheregis a polynomial of degree at mostnwith only real zeros, thenf(k) has only real zeros for allk≥ 0. If the degree ofgisn+1 thenf(k) has only real zeros for allk≥ 0 if, and only iffandf′ have only real zeros.

ISSN:0278-1077    

DOI:10.1080/17476939808815138

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

The representation problem for a meromorphicfon, consists of representingfas the quotientfs;g/hof two entire functionsgandh, each with logarithm of modulus majorized by a function as close as possible to the Nevanlinna characteristic

ISSN:0278-1077    

DOI:10.1080/17476939808815139

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

Suppose thatkis a positive integer and thatfis meromorphic of finite order in the plane, such that g =f(k)/fis transcendental. Ifghas order les than ½ thengmust have infinitely many zeros, and the same conclusion holds iffhas only finitely many poles and lim infr→∞T(r, f)/r= 0.

ISSN:0278-1077    

DOI:10.1080/17476939808815140

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor