摘要:

We prove a generalization toCof a well known theorem [3] that inR, the Riccati equationW1+W2=F2withFreal and positive on the positive real axis, such that limx→+∞F=+∞, has a family of solution asymptotic toFand a unique solution asymptotic to -F.

ISSN:0278-1077    

DOI:10.1080/17476939408814708

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

The sheafF- of quaternionic hyperfunctions is introduced as the sheaf of boundary values of quaternionic regular functions. A Köthe duality type theorem is established to prove the isomorphism between compactly supported quaternionic hyperfunctions and compactly supported regular functionals. Ordinary differential operators are studied on the sheafFwith the use of theC ? Kproduct. Finally a sheaf of quaternionic microfunctions is introduced as the microlocalization ofF, and its main properties are studied.

ISSN:0278-1077    

DOI:10.1080/17476939408814709

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

Using the Nevanlinna theory, we investigate the existence problem of some algebroid solutions of a class of generalized higher order algebraic differential equations and obtain a general Malmquist theorem which extends some earlier results.

ISSN:0278-1077    

DOI:10.1080/17476939408814710

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

It is proved that the module of Clifford-algebra-valued square-integrable eigenfunctions of the Dirac-operator in an open subset Ω ofRmis a Hilbert-module with reproducing kernel; this reproducing kernel for the case where Ω is the unit ball or the Euclidean space itself, is explicitly constructed. Also the module of square-integrable polymonogenic functions inRmis studied. It turns out that it is a Hilbert-module with reproducing kernel too.

ISSN:0278-1077    

DOI:10.1080/17476939408814711

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

We prove that ifis a holomorphic map of the unit ball such thatdf(0) =Iandf(Bn) is convex, then any translation off(Bn) through a distance less than π/2 meetsf(Bn). In contrast to the one-variable situation (studied by MacGregor), the result is not true if the convexity assumption is dropped completely.

ISSN:0278-1077    

DOI:10.1080/17476939408814712

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In this paper, the properties of vector-valued elliptic functions and the stability of integral equations with the kernel ζ-function of a class in a locally convex space are discussed.

ISSN:0278-1077    

DOI:10.1080/17476939408814713

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In the present paper fundamental matrices are constructed by superposition for linear uniformly elliptic systems ofm≥1 complex partial differential equations withBeltramiprincipal part in a domainTwith small measure. A so-calledLevimatrix a fundamental solution for the principal part with ‘frozen’ coefficients—is explicitely determined. The fundamental matrices are obtained by adding a weakly singular term satisfying a system of weakly singular integral equations to the Levi matrix. The coefficient matrix of the principal part is assumed to belong toHLp(T,D)p>2, its derivative with respect to ζ and the coefficients of the lower order terms toL2(D) for someD T. Assumptions concerning the structure of the matrix of coefficients of the principal part are not required. A generalizedPompeiuformula for solutions to the inhomogeneous formally adjoint system is proved.

ISSN:0278-1077    

DOI:10.1080/17476939408814714

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

This paper continues the investigation of uniformly starlike functionsUSTand a class of starlike functionsSp, withzff′(z)/f(z) ranging over a parabolic region. We give an example to show that Sp is not included inUST. This answers a question raised in a previous paper. Further, we give some radius properties in connection with these classes, and finally we investigate uniform starlikeness in relation to the property starlikeness with respect to symmetrical points.

ISSN:0278-1077    

DOI:10.1080/17476939408814715

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

This paper deals with the differential equation, whereAandBare analytic on an angle. Some results concerning the estimates of the growth of solutions of the equation restricted in the angle are obtained. By using these estimates we also improve some known results in the plane case.

ISSN:0278-1077    

DOI:10.1080/17476939408814716

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

A simply connected planar domain Ω of finite area is said to be a Poincare disk if there exists a finite positive constantKsuch thatfor all functionsuwhich areC1on Ω and integrate to zero. In this paper we establish geometric necessary and sufficient conditions for Ω to be a Poincarè disk. Our criteria, which are reminiscent of the isoperimetric inequality and simplify a characterization of Maz'ja, state that the smaller area determined from a crosscut of Ω must be bounded by a constant multiple of the length of the crosscut. We show that this characterization is valid for three different types of crosscuts: line segments, hyperbolic geodesies, and general crosscuts. We also obtain a characterization of those conformal mappings which map the disk onto a Poincarè disk in terms of an integral growth condition. We use techniques from, geometric function theory and hyperbolic geometry.

ISSN:0278-1077    

DOI:10.1080/17476939408814717

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor