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On one representation of analytic functions by harmonic functions
AbstractLet u(x) be a function analytic in some neighborhood D about the origin, $$ \mathcal{D} $$ ⊂ ℝn. We study the representation of this function in the form of a series u(x) = u0(x) + |x|2u1(x)Expand
On the solution of the inhomogeneous polyharmonic equation and the inhomogeneous helmholtz equation
We present formulas that simplify finding the solutions of the Poisson equation, the inhomogeneous polyharmonic equation, and the inhomogeneous Helmholtz equation in the case of a polynomialExpand
Polynomial solutions of the Dirichlet problem for the biharmonic equation in the ball
We find a polynomial solution of the Dirichlet problem for the inhomogeneous biharmonic equation with polynomial right-hand side and polynomial boundary data in the unit ball. To this end, we use theExpand
A Neumann-type problem for the biharmonic equation
We establish the existence and uniqueness of a solution to a Neumann-type problem in the unit ball. An illustrative example is considered.
Solving a Problem of Robin Type for Biharmonic Equation
We investigate existence and uniqueness conditions for solution to one Robin type problem for inhomogeneous biharmonic equation in the unit ball. We construct polynomial solution to the problem whenExpand
Solution of the Dirichlet problem with polynomial data for the polyharmonic equation in a ball
We find a polynomial solution of the Dirichlet problem with polynomial boundary data for the polyharmonic equation with polynomial right-hand side in the unit ball.
SOLVABILITY OF SOME NEUMANN-TYPE BOUNDARY VALUE PROBLEMS FOR BIHARMONIC EQUATIONS
We study some boundary-value problems for inhomogeneous biharmonic equation with periodic boundary conditions. These problems are generalization to periodic data of the Neumann-type boundary-valueExpand
P-LATIN MATRICES AND PASCAL'S TRIANGLE MODULO A PRIME
One of the more effective methods of counting residues modulo a prime in the rows of Pascal's triangle is a reduction of this problem to that of solving of certain systems of recurrence equations.Expand
On one set of orthogonal harmonic polynomials
A new basis of harmonic polynomials is given. Proposed polynomials are orthogonal on the unit sphere and each term of this basis consists of monomials not present in the others. Introduction For theExpand
Construction of polynomial solutions to some boundary value problems for Poisson’s equation
A polynomial solution of the inhomogeneous Dirichlet problem for Poisson’s equation with a polynomial right-hand side is found. An explicit representation of the harmonic functions in the AlmansiExpand
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