Generalized Growth and Approximation of Pseudoanalytic Functions on the Disk

Criterion of the continuation of harmonic functions in the ball of n­dimensional space and representation of the generalized orders of the entire harmonic functions in ℝn in terms of approximation error

“…Expressions for the order and type of solutions of certain linear differential equations in partial derivatives in terms of error in the axisymmetric harmonic polynomial approximation and the Lagrange interpolation were derived in [20]. In [21], a slow growth and the approximation of pseudoanalytic functions on disk were investigated. The necessary and sufficient conditions under which a harmonic function in the ball of a three-dimensional space continues to the entire harmonic one were established in [22].…”

Analog of the classical borel theorem for entire harmonic functions in ℝn and generalized orders

“…Expressions for the order and type of solutions of some linear differential equations with partial derivatives in terms of the error of axisymmetric harmonic polynomial approximation and Lagrange interpolation are obtained in [19]. In [20], slow growth and approximation of pseudoanalytic functions on a disk are studied.…”