摘要:

A necessary and sufficient condition is described for the existence of a function ϕ which is holomorphic and bounded by 1 in a neighborhood of the closed bidisc (D2)-, and which mapsnspecified points in part D2, the topological boundary of D2, tonspecified points in D. Such an interpolating function exisits if and only it a bounded holomorphic interpolating function exists if and only it a bounded holomorphic interpolating function exists separaately on D2and on each analytic disc in ∂D2. The proof uses a limit of Agler's matirx condition for interpolating interior points of D2.

ISSN:0278-1077    

DOI:10.1080/17476939408814704

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In this paper, we first consider the posibility of extending to the exterior of a region the solution to a Dirichlet problem. We limit ourselves to the situation where the boundary curve is analytic and the boundary data is polynomial or real-entire. We then turn to the problem of hte existence of solutions to the functional equationf(P(z))-g(Q(z)) =k(z),, wherePandQare given polynomials andkis a given meromorphic function. Central to our results is a generalization of a theorem of A. and C. Rényiconcerning periodic functions of the formf(P). We conclude by showing how the two problems ae related.

ISSN:0278-1077    

DOI:10.1080/17476939408814705

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In this paper, we describe necessary and sufficient conditions for the linear dependence ofNentire (or smooth) functions inin terms of vanishing of several, conveniently generalized, Wronskians, and prove theversion of the well-known Borel theorem about the linear dependency of exponential functions.

ISSN:0278-1077    

DOI:10.1080/17476939408814706

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939408814693

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor