The Dirac equation for spinor-valued fields $f$ on the Minkowski space of even dimension form a hyperbolic system of partial differential equations. In the paper, we are showing how to reconstruct the solution from initial data given on the upper sheet $H^{+}$ of the hyperboloid. In particular, we derive an integral formula expressing the value of $f$ in a chosen point $p$ as an integral over a compact cycle given by the intersection of the null cone with $H^{+}$ in the Minkowski space $𝕄$.

Integrals of the Cauchy type extended over the boundary $\partial A$ of a general compact set $A$ in the complex plane are investigated. Necessary and sufficient conditions on $\partial A$ are established guaranteeing the existence of angular limits of these integrals at a fixed $z\in \partial A$ for all densities satisfying a Hölder-type condition at $z$.

The paper is a contribution to the complex variable boundary element method, shortly CVBEM. It is focused on Jordan regions having piecewise regular boundaries without cusps. Dini continuous densities whose modulus of continuity $\omega (·)$ satisfies $$\underset{s\downarrow 0}{lim\; sup}\omega \left(s\right)ln\frac{1}{s}=0$$ are considered on these boundaries. Functions satisfying the Hölder condition of order $\alpha$, $0<\alpha \le 1$, belong to them. The statement that any Cauchy-type integral with such a density can be uniformly approximated by a Cauchy-type integral whose density is a piecewise...

The survey collects many recent advances on area Nevanlinna type classes and related spaces of analytic functions in the unit disk concerning zero sets and factorization representations of these classes and discusses approaches, used in proofs of these results.