摘要:

The concepts of generalized order, system of generalized associated orders and generalized order with respect to one variable have been introduced for a class of plurisubharmonic functions. A number of relations involving the above growth constants have been investigated. The results obtained in this paper extend the corresponding results found by Ronkin.

ISSN:0278-1077    

DOI:10.1080/17476938508814123

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

摘要:

Letbe a Blaschke sequence of points in the unit disk, with, such thatconverges to a point ζon the unit circle. We prove that ifthen there exists a pair of bounded univalent functions f andg, with f(0)=g(0)=0 and f′(0)=g′(0)=1, such that f(z)=g(z) if and only if.This result, and another slight extension of this result, gives a partial solution to a problem of P. L. Duren and A. Obrock.

ISSN:0278-1077    

DOI:10.1080/17476938508814124

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

摘要:

In this paper we generalize a Liouville type theorem obtained by Gay in [7] and apply this result to several problems in analysis and mathematical physics such as the non-existence of a smallest carrier for an analytic functional in several dimensions, the determination of the discriminant of Hill's equation and the eigenvalue problem of trace class operators on Hilbert spaces. Furthermore Lerch's theorem obtained in [20] is applied to arithmetic entire functions of exponential type and some interpolation formulas for entire functions of exponential type are established. Finally a characterization is given of analytic functionals with carrier at the origin.

ISSN:0278-1077    

DOI:10.1080/17476938508814125

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

摘要:

The homological version of the Cauchy integral formula is formulated in the paper for solutions of corresponding equations in complexified hypercomplex analysis. Many different cases are treated in unified manner, including some higher order operators. The notion of index ofn-cycles is defined in this complexified situation and its properties are studied.

ISSN:0278-1077    

DOI:10.1080/17476938508814126

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

摘要:

In this paper differential equationswith coefficients analytic inare investigated. We are interested in the case that such an equation has no univalent solution.

ISSN:0278-1077    

DOI:10.1080/17476938508814127

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

摘要:

LetFbe the family of functions schlicht in the annulus R:= {w:ρ<|w|<1} (ρ<) mappingRonto the unit disk minus some continuum. This family of functions was introduced by Gaier [2], and a first distortion theorem was proved by Duren-Schiffer [1], Gaier Huckemann, [3], and independently by Gehring-af Hällström [4]. Here we characterize the familyFand prove a further distortion theorem forF.

ISSN:0278-1077    

DOI:10.1080/17476938508814128

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

摘要:

It is an easy consequence of the second fundamental theorem of Nevanlinna that each derivative, of a transcendental meromorphic functionghas at most one finite Picard value. Generalizing a result of Mues we prove that forg=fn+2only zero can be this Picard value. The functionsf=R expP, RrationalPpolynomial, show that Picard value zero can actually occur. We show that for k⩽n, n⩽3, (fk)(n)has Picard value zero only iffis of this form.

ISSN:0278-1077    

DOI:10.1080/17476938508814129

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938508814122

出版商:Gordon and Breach Science Publishers    

年代:1985

数据来源: Taylor