摘要:

We consider certain functions meromorphic in the plane that are of bounded type in suitable half planes. LetZjbe a sequence in a half plane not satisfying a Blaschke condition there. We deduce that conditions of being positive semi-definite on matrices whose elements depend onzjand the values that such a functionftakes at thezj, determinefuniquely. This can be used to study the properties offfurther. In particular, we give a function theoretic derivation for the fact that a certain set of inequalities is equivalent to Riemann's hypothesis. We also comment on iteration theoretic methods for studying such problems.

ISSN:0278-1077    

DOI:10.1080/17476939708815042

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

Some notions from descriptive set theory are related to the solution-set of a D.E. in a Banach space.

ISSN:0278-1077    

DOI:10.1080/17476939708815043

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

We consider systems of linear differential equations near an irregular singularity of rank one with a leading coefficient matrix having all distinct eigenvalues. The main results express connection coefficients (Stokes' multipliers and connection factors) as sums of convergent series or as limits of sequences, where the terms may be calculated in various ways. One way is to form certain explicit weighted sums of the coefficients in the formal or Frobenius series solutions. Another way is to recursively solve for the coefficients of a solution of a certain singular integral equation similar to the Frobenius method for differential equations near a regular singular point. In case the original differential equation has rational coefficients, then associated linear differential equations with rational coefficients can be constructed whose Frobenius solution determines die terms in the series or limits; hence all transformations are done within the class of “holonomic” functions.

ISSN:0278-1077    

DOI:10.1080/17476939708815044

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

Letfandgbe transcendental meromorphic functions such thatfandgshare the values 0 and ∞ CM and thatf(n)andg(n)share the value 1 CM. Iff≠gandf(n)g(n)≠1 then, apart from one exceptional caseThis result answers a question of Yang and is also related to a result of Yi.

ISSN:0278-1077    

DOI:10.1080/17476939708815045

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

Y. Noda proved that for any given entire functionFthe set ofafor whichF(z)+azis not prime is at most countable. In this paper we prove that the functionG(ez) +azis prime with at most two exceptional valuesawhereG(w)is an entire function satisfyingforR≥R0> 0 and for some constantK>0

ISSN:0278-1077    

DOI:10.1080/17476939708815046

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

A classical result in the theory of elliptical functions states that. The functionK2belongs to an important class of functions called the Schwarzian triangle function, for it maps a curvilinear triangle conformally to the upper half plane. The above identity reveals an interesting relation between a hypergeometric function and a Schwarzian triangle function. The purpose of this paper is to clarify the connection between the hypergeometric functionF((1/2 − (1/2n), (1/2) + (1/2n), 1,zand the associated Schwarzian triangle function. In particular, in Theorem 2, we prove that all the major features of the above classical result remain valid for a class of hypergeometric functions called the Legendre functions.

ISSN:0278-1077    

DOI:10.1080/17476939708815047

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

We find the form of all subnormal solutions of equations (1.1). Our results extend previous results fornthorder homogeneous equations and for second order nonhomogeneous equations. Several examples are given.

ISSN:0278-1077    

DOI:10.1080/17476939708815048

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

For theK-quasiconformal mappings in the complex plane, a precise fundamental inequality is established. From this, the defect relation, filling disks, Borel directions and normal criterion are also derived.

ISSN:0278-1077    

DOI:10.1080/17476939708815049

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939708815031

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor