Obtaining analytic functions and conjugate harmonic functions

Generalized Conjugate and Analytic Functions without Expansions.

On a Lebesgue measure space with measure element do, and total measure finite or infinite, we consider the complex-valued measurable functions f, y, so, ., each determined only a.e., and each belonging to all L,-classes simultaneously, 1<r< a. We donote (i) by F = {f} a ring of functions with complex constants and ordinary multiplication and closed under the involution: if f -= f + if2 e F then...

Conjugate Harmonic Functions and Clifford Algebras

We generalize a Hardy-Littlewood inequality and a Privalov inequality for conjugate harmonic functions in the plane to components of Clifford-valued monogenic functions.

Harmonic and analytic functions on graphs

Harmonic and analytic functions have natural discrete analogues. Harmonic functions can be defined on every graph, while analytic functions (or, more precisely, holomorphic forms) can be defined on graphs embedded in orientable surfaces. Many important properties of the “true” harmonic and analytic functions can be carried over to the discrete setting. We prove that a nonzero analytic function ...

Classical Expansions and Their Relation to Conjugate Harmonic Functions

A Subclass of Analytic Functions Associated with Hypergeometric Functions

In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.