INTEGRAL REPRESENTATIONS OF GENERALIZED HARMONIC FUNCTIONS

On the Integral Representations of Generalized Relative Type and Generalized Relative Weak Type of Entire Functions

In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.

Integral Representations of Harmonic Lattice Sums

On Integral Operator and Argument Estimation of a Novel Subclass of Harmonic Univalent Functions

Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent func...

Sharp integral inequalities for harmonic functions

Motivated by Carleman’s proof of isoperimetric inequality in the plane, we study some sharp integral inequalities for harmonic functions on the upper halfspace. We also derive the regularity for nonnegative solutions of the associated integral system and some Liouville type theorems.

Constructive Nonstandard Representations of Generalized Functions

Using techniques of nonstandard analysis Abraham Robinson showed that it is possible to represent each Schwartz distribution T as an integral T () = R f, where f is some nonstandard smooth function. We show that the theory based on this representation can be developed within a constructive setting.