ISSN:0278-1077    

DOI:10.1080/17476939408814777

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

A simple technique is given for constructing the spherical harmonics as polynomials inRn.

ISSN:0278-1077    

DOI:10.1080/17476939408814778

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

Letfbe analytic in the unit diskEf(0)=0f(z) ≢ 0 otherwise. We consider the problem of estimating the argumentforgiven bounds for. Such problems arise in measuring the accuracy of approximate conformal mappings of simply connected domains onto the unit disk.

ISSN:0278-1077    

DOI:10.1080/17476939408814779

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

We consider systems of linear differential equations with an irregular singular point of Poincaré rank 1 at infinity. It is well known that there is a fundamental system of formal solution vectors and, for each halfplane, a fundamental system of actual solution vectors having the formal ones as asymptotic expansions. These asymptotic expansions (in the sense of Poincaré) describe the behavior of the actual solutions as theindependent variablezgrows indefinitely, but give no precise error bounds for a givenz, if the asymptotic series are truncated afterNterms. In this paper we show that for large values of |z| the best choice ofNis proportional to |z| and that the resulting error terms are exponentially small.

ISSN:0278-1077    

DOI:10.1080/17476939408814780

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

Consider the equationwhose coefficients are entire functions of the variable r = |X| Corresponding to a specified axially symmetric solution Ψ and setCnofn= 1 circles, an axially symmetric solutionis found that interpolates to Ψ(x,p)on theCnand converges uniformly to Ψ(x,p)on certain axiaiiy symmetric domains. An extension is given for a class of solutions with the symmetry requirement relaxed.

ISSN:0278-1077    

DOI:10.1080/17476939408814781

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

The behavior of functions given by series of Laguerre variants is studied by consideringtheir Laplace transforms. They are shown to have singularities at points determined bytheir associated power series. The proof involves the Hadamard-Gilbert rule.

ISSN:0278-1077    

DOI:10.1080/17476939408814782

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

The analytic representation of a function or a distribution on the real line is given in terms of series of ”analytic wavelets.“ These series converge uniformly in compact subsets of the upper and lower half plane. The analytic wavelets used satisfy the same dilation equation as the orthogonal wavelets on the real axis.

ISSN:0278-1077    

DOI:10.1080/17476939408814783

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

The Whittaker-Shannon-Kotel'nikov sampling theorem provides sampling series expansions for the re-construction of functions (signals) that are bandlimited to finite closed intervals, symmetric about the origin, i.e., intervals of type [−a,a]. There are generalizations of this theorem toNdimensions, yet they all mainly deal with functions that are also bandlimited toN-dimensional rectangles symmetric about the origin. No general theory seems to exist for functions that are bandlimited to a general domain inNdimensions. In this paper we give, by using polar coordinates, a sampling series expansion that can be used for the reconstruction of functions (signals) that are bandlimited to a disc centered at the origin. The sample points are the eigenvalues of a Dirichlet problem in the disc.

ISSN:0278-1077    

DOI:10.1080/17476939408814784

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939408814776

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor