摘要:

We consider the Poincaré series operator Θ as a holomorphic mapping of the Teichmüller space T(Γ) of a Fuchsian group Γ into the Bers spaceA(Γ) of integrable holomorphic quadratic forms, and show that if Γ is finitely generated and of the first kind, then ⊖ gives a local coordinate ofT(Γ) at the origin. Conversely, if Θ(T(Γ)) contains an interior point in A(Γ), then Γ is finitely generated and of the first kind.

ISSN:0278-1077    

DOI:10.1080/17476939308814609

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

In this note, invariant superharmonic functions with respect to the Bergman metric on a bounded domain inare considered. It proves a uniqueness theorem for nonnegative invariant superharmonic functions on a bounded domain with-boundary. In particular, the corresponding result on the unit ball is proved.

ISSN:0278-1077    

DOI:10.1080/17476939308814610

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

The Loewner equation is used to derive an interesting differential equation relating the endpoints of single slit conformal mappings. Two brief applications follow.

ISSN:0278-1077    

DOI:10.1080/17476939308814611

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

The present paper is a continuation of [8], where the Riemann—Hilbert problem for generalized Cauchy—Riemann systems is considered. The main result of [8] is a criterion for the Fredholm property of this boundary value problem.

ISSN:0278-1077    

DOI:10.1080/17476939308814612

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

This paper is devoted to study the existence of singularities of series expansions in Laguerre polynomials of holomorphic functions on the boundaries of its natural region of convergence. An Equiconvergence theorem is proved by which the convergence problem of Laguerre series can be reduced to the simpler discussion of the convergence of associated with them trigonometric series. Based on this the existence of Laguerre series having no finite singular points is established. A theorem is also proved which makes us sure that as inthe case for power series, for the analytic continuation of functions defined by series in Laguerre polynomials it can be judged by the properties of the series coefficients. The final section of the paper contains some proposals as a result of applying the classical method of constructing non-continuable series by means of gaps.

ISSN:0278-1077    

DOI:10.1080/17476939308814613

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

LetCbe a regular cone inand in some instances a more general proper open connected subset of. We study holomorphic functions in tubeswhich satisfy a norm growth inLrwith the bound involving the associated functionM*(ρ) corresponding to sequencesMpp= 0,1,2,…, which are used to define ultradistributions. We show that these holomorphic functions haveFourier–Laplace integral representations and obtain boundary values in the ultradistribution spaces of Beurling typeD′((MP),Lr) which are generalizations of the Schwartz distributionsD′Lr. TheLrnorm growth which we study here is motivated by the norm growth proved here for the Cauchy integral of elements inD′(*,Lr), where * is either (Mp) or {Mp}, ultradistributions of Beurling type or Roumieu type, respectively.

ISSN:0278-1077    

DOI:10.1080/17476939308814614

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

Rational representations are obtained for the functions

ISSN:0278-1077    

DOI:10.1080/17476939308814615

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

Let Ω be a positive measure on the unit ball U of CNsatisfying Békollé'sBp(β) condition. We characterize those positive measures μ on U such that the inequalityholds for every functionfin the weighted Bergman spaceAp(Ω). As an application, we characterize the multipliers fromAp(Ω) toAq(Ω) (1<p≤q<∞).

ISSN:0278-1077    

DOI:10.1080/17476939308814616

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

This paper studies the zero sets of the Fock spaces. We show that-zero sets are different fromzero sets ifp ≠ q; the union of two-zero sets is not an-zero set in general; and a subset of an-zero set is not necessarily an-zero set. We also show that if {zn} is an-zero set (not containing the origin) with multiple zeros repeated and modulus in increasing order then there exists a constant ε> 0 such thatfor alln>1.

ISSN:0278-1077    

DOI:10.1080/17476939308814617

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

In this paper we generalize the Vekua II-Operator to. Furthermore, its properties investigated in detail. Finally we provide an application to global solutions for higher dimensional Beltrami equations.

ISSN:0278-1077    

DOI:10.1080/17476939308814618

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor