ISSN:0278-1077    

DOI:10.1080/17476938708814244

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Suppose that ƒ is an analytic function in a domain, Ω, of finite connectivity. We give a criterion for a decomposition of ƒ, as a polynomial of another function, that is restricted to a continuum in Ω, to extend to the rest of Ω. We show by examples that this criterion cannot be improved. In the case ƒ has finitely many critical values in Ω, we conclude a necessary and sufficient condition for ƒ to be a polynomial of a locally univalent function. Also, we give a criterion for ƒ not to have the latter decomposition.

ISSN:0278-1077    

DOI:10.1080/17476938708814245

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938708814246

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

We Present the necessary and sufficient conditions for a sequence to be the moment sequence of a distribution in the space of the distributions of compact support. The analysis is based on a series of lemmas that reduce the problem to that of existence of distributional boundary limits of certain analytic functions defined in the unit disk. These results have many applications. We give an application in the theory of orthogonal polynomials.

ISSN:0278-1077    

DOI:10.1080/17476938708814247

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Letbe the space of entire functions with growth conditions introduced by Hörmander. Iff…fmgbelong to, let us consider the following condition:for some ε, C > 0.

ISSN:0278-1077    

DOI:10.1080/17476938708814248

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

The notion of proximate order for an entire Dirichlet series with index-pair (p−q) is introduced and its existence theorem is proved by an elementary technique. The (p,q) proximate order is a class of entire Dirichlet series is constructed under certain conditions Also, the lower (pq)-proximate order is defined and its existence theorem is stated. The authors remark that there exist two proximate orders for a given entire Dirichlet series with index-pair (p,q) and present conditions under which both comparison functions coincide. In the last section, the possibility of approximating a generalized proximate order by some other proximate order is searched.

ISSN:0278-1077    

DOI:10.1080/17476938708814249

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Nonlinear difference equations of the formare studied under suitable assumptions on the function G(w) and the roots of the polynomial. Equation (I) is reduced to an operator equation of the formwhereg1is a fixed element in an abstract. Banach spaceH1and depends on the initial conditions (f(i) = λii=1, 2….kof (I). The existence of a solutionfof (II) inH1means that there exists a solutionf(n) of (I) such that the power seriesconverges absolutely for |z|⩽.1. In the case of the linear homogeneous or inhomogeneous equationthe nonlinear operator N1in (II) is a constant mapping inH1and (II) gives the abstract formfof the unique solutionf(n). A theorem for the existence of solutions of (IV) in the Hilbert space l2(1,∞) and the Banach space l1(1∞) follows immediately from this result. Two corollaries to this theorem predict the radius of convergence of the series (III) and a third corollary predicts the existence of “chaotic motion” in a class of nonhomogeneous linear difference equations. For the case, where the functionG(w) is analytic, it is shown that the nonlinear operator, is a holomorphis map in an open sphere ofH1. This proves the existence of solutions in l1(1, ∞) of the more general nonlinear equationunder suitable assumptions on the sequencesck(n)k= 1,2,….

ISSN:0278-1077    

DOI:10.1080/17476938708814250

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

A nonlinear diffusion equation proposed by Satsuma and Mimura is reduced to a Hammerstein integral equation for an analytic function in the spatially periodic case. By means of Schauder's and Banach's fixed point theorem existence and uniqueness of a solution to the Hammerstein equation are proved.

ISSN:0278-1077    

DOI:10.1080/17476938708814251

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Suppose thatFis univalent in the open unit diskU. the complement ofF(U) is a convex set which is not a ray and that the boundary ofF(U) satisfies a smoothness condition at ∞ Lets(F) denote the set of functions subordinate toF.Hs(F) the closed convex hull ofs(F)) andEHs(F))) the set of extreme pointsHs(F). We prove that

ISSN:0278-1077    

DOI:10.1080/17476938708814252

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

All univalent entire functions are linear and maponto itself. In this note we give a characterization of the class of locally univalent entire functions mappingonto. In particular, the functionbelongs to this class.

ISSN:0278-1077    

DOI:10.1080/17476938708814253

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor