On cyclic and radial variations of a plane path (Preliminary communication)
On definitions of superharmonic functions
Let be an elliptic differential operator of second order with variable coefficients. In this paper it is proved that any -superharmonic function in the Riesz-Brelot sense is locally summable and satisfies the -superharmonicity in the sense of Schwartz distribution.
On definitions of the pluricomplex Green function
We give several definitions of the pluricomplex Green function and show their equivalence.
On determining a riemannian manifold from the Dirichlet-to-Neumann map
On discrepancy theorems with applications to approximation theory
We give an overview on discrepancy theorems based on bounds of the logarithmic potential of signed measures. The results generalize well-known results of P. Erdős and P. Turán on the distribution of zeros of polynomials. Besides of new estimates for the zeros of orthogonal polynomials, we give further applications to approximation theory concerning the distribution of Fekete points, extreme points and zeros of polynomials of best uniform approximation.
On duality and interpolation for spaces of polyharmonic functions
On essential norm of the Neumann operator
One of the classical methods of solving the Dirichlet problem and the Neumann problem in is the method of integral equations. If we wish to use the Fredholm-Radon theory to solve the problem, it is useful to estimate the essential norm of the Neumann operator with respect to a norm on the space of continuous functions on the boundary of the domain investigated, where this norm is equivalent to the maximum norm. It is shown in the paper that under a deformation of the domain investigated by a diffeomorphism,...
On Exceptional Sets for Superharmonic Functions in a Halfspace: An Inverse Problem.
On existence in the Cauchy problem for the biharmonic equation
On exit laws for semigroups in weak duality
Let be a measurable semigroup and a -finite positive measure on a Lusin space . An -exit law for is a family of nonnegative measurable functions on which are finite -a.e. and satisfy for each
On exit laws for subordinated semigroups by means of -subordinators
We study the integral representation of potentials by exit laws in the framework of sub-Markovian semigroups of bounded operators acting on . We mainly investigate subordinated semigroups in the Bochner sense by means of -subordinators. By considering the one-sided stable subordinators, we deduce an integral representation for the original semigroup.
On extensions of the Mittag-Leffler theorem
The classical Mittag-Leffler theorem on meromorphic functions is extended to the case of functions and hyperfunctions belonging to the kernels of linear partial differential operators with constant coefficients.
On extremal problems related to inverse balayage.
On Fatou-Type Theorems for Non-Radial Kernels.
On functions with bounded mixed variance
On generalized Fatou theorems for the square root of the Poisson kernel and in rank one symmetric space
On global Sobolev inequalities.
On Hadamard's problem for higher dimensions.
On Hardy type inequality with non-isotropic kernels.
On harmonic conjugates with exponential mean growth