Properties of the Cauchy–Riemann–Fueter equation for maps between quaternionic manifolds are studied. Spaces of solutions in case of maps from a K3–surface to the cotangent bundle of a complex projective space are computed. A relationship between harmonic spinors of a generalized nonlinear Dirac operator and solutions of the Cauchy– Riemann–Fueter equation are established.

Using the fixed point method, we prove the Hyers–Ulam stability of the Cauchy–Jensen functional equation and of the Cauchy–Jensen functional inequality in fuzzy Banach ∗-algebras and in induced fuzzy C-algebras. Furthermore, using the fixed point method, we prove the Hyers–Ulam stability of fuzzy ∗-derivations in fuzzy Banach ∗-algebras and in induced fuzzy C-algebras. Published by Elsevier Ltd

Let (Ω, M, µ) be a measure space. Then for any two complex valued measurable functions f and g, we have the Cauchy-Schwarz inequality: 0.1 THEOREM (Cauchy-Schwarz inequality). Let (Ω, M, µ) be a measure space. Then for any two complex valued measurable functions f and g such that

We describe an algorithm for the reconstruction of the equilibrium in a Tokamak from discrete magnetic measurements. In order to solve this inverse problem we first use toroidal harmonics to compute Cauchy boundary conditions on a fixed closed contour. Then we use these Cauchy boundary conditions to solve a non-linear source identification problem.

In this paper, which is essentially a survey, we solve the global Cauchy problem on causal manifolds for hyperbolic systems of linear partial differential equations in the framework of hyperfunctions. Besides the classical Cauchy–Kowalevsky theorem, our proofs only use tools and ideas of purely algebraic and geometric nature from the microlocal theory of sheaves. Mathematics Subject Classificat...

The Cauchy problem for certain non-Kowalevskian complex homogeneous linear partial differential equations with constant coefficients is considered. The necessary and sufficient conditions for the Borel summability is given in terms of analytic continuation with an appropriate growth condition of the Cauchy data.

This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace’s equation in domains with C boundary. It is an extension of an earlier result of [19] for domains of class C. Our estimate is established by using a global Carleman estimate near the boundary in which the exponential weight depends on the distance function to the boundary. Further...