摘要:

We have proved that provided a space of pseudoholomorphic functions is given, one can construct operatorsLsuch that the initial-value problem of Cauchy-Kowalewski typeturns out to be solvable in any case. The solution belongs to the subspace defined by the ordinary differential equation of the formwheredEw/dzdenotes theE-derivative of theE-pseudoholomorphic functionw.

ISSN:0278-1077    

DOI:10.1080/17476939608814940

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

In this paper we complete the description of Mergelyan sets for the harmonic Hardy spaceh∞(B) of bounded harmonic functions in the unit ballBof, initiated in [10]. We also characterize those relatively closed subsetsXof a bounded open set ω in the complex plane such that any harmonic functionfon ω can be approximated uniformly on compact subsets of ω by harmonic polynomials and, simultaneously, the same sequence of polynomials converges tofuniformly onxor in Lipschitz norm onXwhenever, respectively, the restriction offtoXis uniformly continuous, or is in lip(αX), 0 > α > 1/2.

ISSN:0278-1077    

DOI:10.1080/17476939608814941

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

It is known that there is a one-to-one correspondence between a subclass of distributions and the space of entire functions of exponential type via Fourier Transforms. In this paper, this correspondence has been extended to generalized functions.

ISSN:0278-1077    

DOI:10.1080/17476939608814942

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

In this paper we show that a pseudoconvex Riemann domain containing the product space of a real domain and a complex vector spaceEis the product space of a pseudoconvex Riemann domain andE.

ISSN:0278-1077    

DOI:10.1080/17476939608814943

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

In this paper we investigate radial and tangential limits of pluri-Green potentialsVμon the unit ballBin, which for suitableμare defined bywhere forzεB,φzdenotes the holomorphic automorphism ofBsatisfying φz(0)=z, φz(z) = 0, and φz(φz(w))=w. The main result of this paper is as follows: Let λ be theM-invariant measure onBand letfbe a non-negative measurable function onBsatisfying, andfor somep<1, then the pluri-Green potentialVfhas tangential limit at almost all points of the boundarySofB. It is shown that the result is best possible.

ISSN:0278-1077    

DOI:10.1080/17476939608814944

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

LetGbe the set of all nontrivial points inM(H∞), the maximal ideal space ofH∞. An interpolating Blaschke productbis called typeGif. The purpose of this paper is to give some equivalent conditions on interpolating Blaschke products to be typeGand give some classifications of interpolating Blaschke products of typeG.

ISSN:0278-1077    

DOI:10.1080/17476939608814945

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

We prove that the group of Clifford matrices SL(2,гn) is isomorphic to a subgroup of Lie group GL(2n,R). Using this result, a generalization of Jørgensen inequality of discrete Möbius groups in all dimensions is obtained.

ISSN:0278-1077    

DOI:10.1080/17476939608814946

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

In iteration theory of rational, entire and meromorphic functions it is well known that the Julia set is the closure of the set of repulsive periodic points. Whereas the proof in the rational case is elementary, the original proofs in the entire and meromorphic case both rely on a deep theorem of Ahlfors, the five island theorem. Recently, Schwick [7] gave a very nice elementary proof for the entire case. Using a result of Lehto and Virtanen, we can extend his proof even beyond the classical meromorphic case.

ISSN:0278-1077    

DOI:10.1080/17476939608814947

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

In this paper it is proved that every paper holomorphic self mapping of a certain Hartogs domain is biholomorphic.

ISSN:0278-1077    

DOI:10.1080/17476939608814948

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

LetMbe the family of all compact sets inwhich have connected complements. ForKεMletA(K) be the Banach space of all functions which are continuous onKand holomorphic in its interior. If φ is an entire function then we denote by φ(j)its derivative of orderjifand a “normalized” antiderivative of order −j.

ISSN:0278-1077    

DOI:10.1080/17476939608814949

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor