摘要:

We consider partial differential equations of second order of formally-hyperboiic or elliptic type which possess differential operators after K. W. Bauer for the representation of its solutions. These operators act on the space of holomorphic functions. Relations between the solutions and the functions generating them are derived. With this it is possible to give general representation theorems for solutions defined in the neighbourhood of isolated singularities. Doing so we discuss unique solutions as well as branched ones.

ISSN:0278-1077    

DOI:10.1080/17476938708814230

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

It is shown that the complex Riemann function of a formally hyperbolic differential equation can be determined by differential operators if a representation of solutions is possible by at least one differential operator acting on an arbitrary holomorphic function. The application of this method is illustrated by several examples.

ISSN:0278-1077    

DOI:10.1080/17476938708814231

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Every open Riemann surfaceRof finite genus can be continued to a closed Riemann surface of the same genus. This classical result is usually proved by a local argument: one considers only a planar neighborhood of the ideal boundary ofRand applies the generalized uniformization theorem of Koebe. In the present paper we prove a continuation theorem of a global character: Let there be given a meromorphic functionfonRwith a special boundary behavior. Im(dfshall be a distinguished harmonic differential of Ahlfors. Then there exists a closed Riemann surfaceR*of the same genus asRand a meromorphic extensionf*offontoR*such that (i)R*\Rhas a vanishing area, (ii)f*is holomorphic onR*\R, and (iii) Imf*assumes a constant value on each boundary component ofRwith respect toR*Since ƒ describes a hydrodynamic phenomenon onR, we callR*a hydrodynamic continuation ofRwith respect tof. The ideal boundaryRis then realized onR*as a set of arcs on the streamlines offwith a total vanishing area.

ISSN:0278-1077    

DOI:10.1080/17476938708814232

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

ForFanalytic inletforandan infinite set. Δ(F) consists of a Jordan curve γ⊂Dand a finite number of points in the bounded component Г of. It is shown that.

ISSN:0278-1077    

DOI:10.1080/17476938708814233

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

In this paper some relaxation of conditions that make a function monogenic is considered in Clifford analysis. Two forms of the Looman Menchoff theorem for monogenic functions are demonstrated. They are generalizations of the Looman Menchoff theorem of complex analysis.

ISSN:0278-1077    

DOI:10.1080/17476938708814234

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

In this paper we present some partial results for the following conjecture of L. Brickman: IfP≢0 is a polynomial of degreenwithP(0) = 0 and α∈(0,π) then there exists an arc Γ on |z|=1 of length at least 2α/nsuch that |arg(P(z))|≦α, z∈Γ.

ISSN:0278-1077    

DOI:10.1080/17476938708814235

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Using the decomposition of the elementary solution of the Dirac operator in plane wave type monogenic functions, we obtain an extension of the classical Radon transform in Euclidean space to the analytic functional of Clifford analysis. This includes, as a special case, the Radon transform of compactly supported hyperfunctions.

ISSN:0278-1077    

DOI:10.1080/17476938708814236

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

The concept of generalized type, system of generalized associated types and the generalized type with respect to one of the variables is being introduced, for a class of plurisubharmonic functions. An upper-bound for the generalized type with respect to one of the variables, as well as few geometric properties of the hypersurface of generalized associated types are found. The results obtained here generalize the results found by Ronkin

ISSN:0278-1077    

DOI:10.1080/17476938708814237

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938708814238

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Let ϕ and ψ be positive continuous functions on [0, 1) with ϕ(r) →0 as r→1 at least as fast as (1−r)a, but no faster than some other power (1−r)b, 0>a>b, and ϕ(r)ψ(r)=(1−r2)α, for some α>b. We first show that there are bounded projections fromLp,q, 1⩽p⩽∞,1⩽q⩽∞, the mixed-norm space of measurable functions on the unit ballBin CN, N ⩽ 1, onto Hp,q(ϕ), the mixed-norm space of analytic functions onB. Using these projections, we show that the dual ofHp-q(ϕ), 1 ⩽p⩽∞, 1⩽q>∞, is topologically isomorphic toHp,q(ψ), 1/p + 1/p′= 1, 1/q+1/q′=1.

ISSN:0278-1077    

DOI:10.1080/17476938708814239

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor