摘要:

In this paper, we deal with the problem of uniqueness of meromorphic functions that share one or two values and obtain some results that are improvements of that of M. Ozawa, H. Ueda, G. Brosch, H. X. Yi and other authors. An example is provided to show that our results are sharp.

ISSN:0278-1077    

DOI:10.1080/17476939508814833

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

This paper studies the unique range sets of entire or meromorphic functions and shows that there exists a finite setSwith 13 elements such that for any two nonconstant meromorphic functionsfandgthe conditionEf(S)=Eg(S)impliesf≡g. As a special case this also answers an open question posed by Gross about entire functions.

ISSN:0278-1077    

DOI:10.1080/17476939508814834

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

It is shown that a known extension of a classical theorem of Laguerre from polynomials to entire functions of exponential type is an easy consequence of a basic result of B. Ja. Levin. Also a supplement to the theorem is obtained.

ISSN:0278-1077    

DOI:10.1080/17476939508814835

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Differential fields of germs of continuous real valued functions of one real variable (Hardy fields) have the property that all elements have limits in the extended real numbers and thus have acanonicalvaluation. For differential fields of holomorphic germs this is not generally the case. We provide a criterion for differential fields of holomorphic germs for its elements to have uniform limits in a partial neighborhood of infinity as an extended complex number.

ISSN:0278-1077    

DOI:10.1080/17476939508814836

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

It is shown in this paper that there exists a nonpositive densityQ(x)inwith the following properties. The cone of positive solutions of (−δ +Q(x))u(x) = 0 inUswith vanishing boundary values onis generated by a single element for everysin (0,1), but there exists no positive solutions of (−δ +cQ(x))u(x) =0 inUsfor anyc> 1 and arbitrarysin (0,1).

ISSN:0278-1077    

DOI:10.1080/17476939508814837

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

A classical I. Schur algorithm describing the Taylor coefficient sequences for bounded in the unit disk analytic functions is generalized to the case when functions take on values in a complex Banach spaceE. LetH∞(E) be the space ofE-valued bounded analytic in the unit disk functions; ρH∞(E)→Enbe the mapping that maps eachfεH∞(E) to its firstntaylor coefficients;B(En) be thep-image inEof the closed unit bail inH∞(E). The description of the boundary and interior point of the setB(En) in a term of a recursion process (a generalized Schur algorithm) is given for the case when the group of diffeomorphisms acts transitively inside the unit ball of Banach spaceE. A case of an arbitrary infinite-dimensional complex Hilbert space of function values also has been considered. The theorem and its corollary are presented which make it possible to reduce the problem lo the corresponding one for bounded analytic functions taking on values in a finite-dimensional Euclidean space, the latter having been completely solved in [2, 3, 7].

ISSN:0278-1077    

DOI:10.1080/17476939508814838

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939508814832

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor