摘要:

For the central index ν of a transcendental integral functionw(z)holdsfor all ξ withexcept for a real set δ of finite logarithmic measure. By the substitution (1) the differential equationwith polynomial coefficients of degrees α is transformed intoStarting from this result it is the main purpose of this paper to deduce the asymptotic relationby an elementary method. This formula leads to the theorem of Wiman: All transcendental integral solutions of (D) are of finite rational order and mean type. Their orders can be determined by the Puiseux-diagram.

ISSN:0278-1077    

DOI:10.1080/17476938408814078

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

We consider analytic solutions of the heat equationuxx+uyy=utdefined in a cylinder and show that any such solution can be expanded in a series of polynomial solutions to the heat equation. If we define the independent complex variableszand[zbar]by =z=x+iy,[zbar]x−ywherexandyare independent complex variables, it is shown that any real-valued analytic solution of the heat equation is uniquely determined by its values on[zbar]=0 ori=0. Using this result, and expressing the above mentioned polynomial solutions to the heat equation in terms of Laguerre polynomials, we obtain some generating functions for Laguerre polynomials, as well as connection formulas between products of Hermite polynomials and Laguerre polynomials of argumentr2=x2+y2. These connection formulas generalize a well known result of Feldheim.

ISSN:0278-1077    

DOI:10.1080/17476938408814079

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

Many functionals on the space of bounded analytic functions on an annulus are defined in terms of a multiplier sequence for the Laurent series. This paper studies the norms of such functionals in terms of a real valued function which induces the functional by integration along the boundary. An application is that symmetric partial sums of the Laurent series give functionals of norm 1 on proper subannuli. Another is a characterization of the Hilbert space operators having the annulus as a spectral set.

ISSN:0278-1077    

DOI:10.1080/17476938408814080

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

It is known that ifis an inner function and ifor if, then ϕ must be a Blaschke product. In this paper we show that if ϕ is an inner function and if

ISSN:0278-1077    

DOI:10.1080/17476938408814081

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

The object of this article is to prove the uniqueness of the composition ƒ − ρ ∞ φ, where ρ is a polynomial of degree at most ρ and φ is a normalized univalent function, whenever ƒ is a close-to-convex function of order ρ. We also give an example of a weakly close-to-convex function ƒ = ρ∞φ with four critical points, and for which ρ is a polynomial of degree five, φ is a normalized univalent function, but the composition is not unique.

ISSN:0278-1077    

DOI:10.1080/17476938408814082

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

A class of nonlinear Riemann–Hilbert problems for one holomorphic function and for a system of such ones is dealt with. By means of a novel application of Schauder's and Tikhonov's fixed point theorem existence of a solution to these problems is proved.

ISSN:0278-1077    

DOI:10.1080/17476938408814083

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

Number theoretic criteria are given for (i) when a (hyperbolic) line in the Poincaré half plane represents symmetric tori and (ii) when a hyperbolic transformation has a glide reflection as a square root. We also give simple constructive proofs of some classical results on the representation of a number by quadratic forms.

ISSN:0278-1077    

DOI:10.1080/17476938408814084

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938408814077

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor