摘要:

I construct a class of functions, whose germs belong to Hardy fields and all of whose derivativesa fortioriultimately exist, but the functions are not ultimatelyC∞. The existence of such functions, while counter-intuitive at first glance, is explained by the fact that the higher order derivatives exist in progressively smaller neighborhoods of +∞ A function not a Hardy field satisfying the required smoothness properties was given in [1]. I provide a proof of the required smoothness properties or this function (omitted in [I]), and then use this function in the present construction.

ISSN:0278-1077    

DOI:10.1080/17476939708814975

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

This paper deals with a generalization of the Pompeiu formula for partial differential equation with higher order in thendimensional complex space. In the centre of the investigation lies a construction of a fundamental solution. The problem of constructing such a fundamental solution can be reduced to solving a special initial value problem. This solution will be turned out to be a generalized Riemann-Vekua-function. With the help of the fundamental solution an integral representation for functions being smooth enough can be found. Functions, which are generalizations to higher dimensions of the polyanalytic or polyharmonic functions in the complex plane, can be represented by the boundary values of the function and some of its derivatives.

ISSN:0278-1077    

DOI:10.1080/17476939708814976

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

A Bl-packing is a (branched) circle packing that “properly covers” the unit disc. We establish some fundamental properties of such packings. We give necessary and sufficient conditions for their existence, prove their uniqueness, and show that their underlying surfaces, known as carriers, are quasiconformally equivalent to surfaces of classical Blaschke products. We also extend the approximation results of to general combinatorial patterns of tangencies in Bl-packings. Finally, a branched version of the Discrete Uniformization Theorem of [1] is given.

ISSN:0278-1077    

DOI:10.1080/17476939708814977

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

The author proved in [4] that a family ofFof meromorphic functions in a domainGis normal. iffandf(k)– ψ have no zeros for eachfψF, where ψ is a fixed analytic function inGwith ψ ≢ and. In this paper the result is generalized to the case that ψ is meromorphic inG. We need the additional assumption thatfand ψ have no common poles for eachfψF.

ISSN:0278-1077    

DOI:10.1080/17476939708814978

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In [7] we obtained, as a consequence of the Fourier transform theory developed in the paper, a sufficient and necessary condition on a sequence (bn)ψl∞for the functionto be holomorphicaily extensible to a heart-shaped region containing the set, and dominated byC/|1-z| whenzis near 1 in the region. This note generalizes this result to the cases when. It also includes corresponding results for series of negative powers and for Laurent series as well. The theory has applications to singular and fractional integrals on closed Lipschitz curves which are closely related io boundary value problems in Lipschitz domains.

ISSN:0278-1077    

DOI:10.1080/17476939708814979

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In this paper the author obtains some conditions of spirallikeness for mappings defined on some bounded domains in.

ISSN:0278-1077    

DOI:10.1080/17476939708814980

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

LetDbe a Hartogs domain in, whereGis a domain in the complex plane, and σ is a positive and continuous function inG. Givensetbe the set of allsuch thatDwis not empty andis notL2-integrabie inDw. We show that if σ is strictly subharmonic inG, then for every closed or open subsetEofGthere exists a functionf. holomorpnic inD. such thatE(D. f)=E

ISSN:0278-1077    

DOI:10.1080/17476939708814981

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In this paper we study strongly annular solutions of the functional equation,g(Z)=f(z)g(zp) wheregandfare both holomorphic functions on the open unit disk andpis an integer greater than or equation to 2 We show that if the function (z) grows rapidly enough as the boundary of the disk approached the approached the solution of the functional equationg(Z), will be a strongly annular function

ISSN:0278-1077    

DOI:10.1080/17476939708814982

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939708814974

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor