A Geometric Property of Functions Harminic in a Disk.
A Hardy space related to the square root of the Poisson kernel
A real-valued Hardy space related to the square root of the Poisson kernel in the unit disc is defined. The space is shown to be strictly larger than its classical counterpart H¹(). A decreasing function is in if and only if the function is in the Orlicz space LloglogL(). In contrast to the case of H¹(), there is no such characterization for general positive functions: every Orlicz space strictly larger than L log L() contains positive functions which do not belong to , and no Orlicz space...
A heat approximation
The Fourier problem on planar domains with time variable boundary is considered using integral equations. A simple numerical method for the integral equation is described and the convergence of the method is proved. It is shown how to approximate the solution of the Fourier problem and how to estimate the error. A numerical example is given.
A Hilbert Lemniscate Theorem in
For a regular, compact, polynomially convex circled set in , we construct a sequence of pairs of homogeneous polynomials in two variables with
A large Wiener sausage from crumbs.
A Levy-Khinchin Formula for Semigroups with Involutions.
A Local Property of L-regular Sets.
A Local Version of Levenberg's Theorem on Determining Measures and Leja's Polynomial Condition.
A lower bound for the gradient of -harmonic functions.
A maximum principle for biharmonic functions in Lipschitz and C1 domains.
A mean value property of harmonic functions on prolate ellipsoids of revolution.
A mixed boundary value problem for heat potentials (Preliminary communication)
A mixed boundary value problem for Laplace's equation involving a nearly circular disk.
A mixed finite element method for the biharmonic problem
A mixed-Lagrange multiplier finite element method for the polyharmonic equation
A Multilevel Algorithm for the Biharmonic Problem.
A Nevanlinna theorem for superharmonic functions on Dirichlet regular Greenian sets
A generalization of Nevanlinna’s First Fundamental Theorem to superharmonic functions on Green balls is proved. This enables us to generalize many other theorems, on the behaviour of mean values of superharmonic functions over Green spheres, on the Hausdorff measures of certain sets, on the Riesz measures of superharmonic functions, and on differences of positive superharmonic functions.
A new characterization of the analytic surfaces in that satisfy the local Phragmén-Lindelöf condition
We prove that an analytic surface in a neighborhood of the origin in satisfies the local Phragmén-Lindelöf condition at the origin if and only if satisfies the following two conditions: (1) is nearly hyperbolic; (2) for each real simple curve in and each , the (algebraic) limit variety satisfies the strong Phragmén-Lindelöf condition. These conditions are also necessary for any pure -dimensional analytic variety to satisify .
A new class of harmonic multivalent functions defined by an integral operator.
A new necessary condition for analytic varieties satisfying the local Phragmén-Lindelöf condition
For an analytic variety V in ℂⁿ containing the origin which satisfies the local Phragmén-Lindelöf condition it is shown that for each real simple curve γ and each d ≥ 1 the limit variety satisfies the strong Phragmén-Lindelöf condition (SPL).