Generalized Cauchy-Riemann Equations Research Articles

Removable Sets for Pointwise Solutions of the Generalized Cauchy-Riemann Equations

We shall operate in N-dimensional euclidean space EN, N _ 2, and use the following notation. x = (xI, *.* , XN) and B(x, r) = the open N-ball with center x and radius r. Also, we shall adopt the convention that if P(x) is a polynomial of degree less than zero, then P(x) is identically zero. We say the function f(x) is in T'(x,), a c N, if f(x) is in L' in a neighborhood of the point x0, and if there is a polynomial P(x) of degree strictly less than a such that

On subharmonicity inequalities involving solutions of generalized Cauchy-Riemann equations

On subharmonicity inequalities involving solutions of generalized Cauchy-Riemann equations

From Generalized Cauchy-Riemann Equations to Linear Algebras

From Generalized Cauchy-Riemann Equations to Linear Algebras

From generalized Cauchy-Riemann equations to linear algebras

In a previous paper [1] the author gave a definition of analytic function in linear associative algebras with an identity. With each such algebra there was associated a set of partial differential equations called generalized Cauchy-Riemann differential equations which serve as a criterion to determine whether a given function is analytic in that algebra. A simplification for the commutative case has been given by Wagner [2]. The purpose of this paper is to give sufficient conditions (Theorem 2) that a set of equations