Band 28, Heft 2

We consider the Dirichlet problem for graphs of prescribed mean curvature in ℝ n +1 where the prescribed mean curvature function H = H ( X , N ) may depend on the point X in space and on the normal N of the graph as well. In some special cases this Dirichlet problem arises as the Euler equation of a generalised nonparametric area functional.

In this paper, the value distribution of the two differential monomials Φƒ n ƒ '[ ƒ ( k ) ] p and Φƒ n -1 ƒ ( k ) are considered, where ƒ is a transcendental meromorphic function, Φ is a non-zero meromorphic function such that T ( r,Φ )= S ( r, ƒ ) as r →+∞, possibly outside a set of r of finite linear measure, n , k and p are positive integers. We also prove K. W. Yu's conjecture [11] in an improved form.

The goal of this paper is to solve the Caratheodory interpolation problem in the class R q [ a,b ] of matrix-functions with the help of the V. P. Potapov´s fundamental matrix Inequality method. In the completely indeterminate case, the general solution is described in terms of a linear fractional transformation.

We consider the asymptotic of the sum of values of the periodic zeta-function L ( s , λ ) over nontrivial zeros of the Riemann zeta-function ζ ( s ). J. Steuding for rational λ obtained the main term. Assuming the Generalized Riemann Hypothesis we calculate the next term.

In this paper we investigate different representation formulae for Stokes flows. We prove their equivalence for three dimensional star-shaped domains, and give a possible generalization for arbitrary spatial domains. We develop similar representations also for the solution of Navier's equation for linear elasticity for spatial and plane domains as well.

We analyze the polynomials H n r ( x ) considered by Gould and Hopper, which generalize the classical Hermite polynomials. We present the main properties of H n r ( x ) and derive asymptotic approximations for large values of n from their differential-difference equation, using a discrete ray method. We give numerical examples showing the accuracy of our formulas.

Applying a generalised Dirichlet's test established for rectangular multiple series, we obtain several new convergence theorems for Lebesgue integrals.

Let ƒ be a function transcendental and meromorphic in the plane and let where a and the coefficients a j and b j are meromorphic functions of small growth compared to ƒ . Under appropriate conditions on the integers m , k and n , estimates are given for the frequency of zeros of ψ in terms of the growth of ƒ .