In this paper we investigate prime divisors, $B_w$-primes and $zs$-primes in $C$-lattices. Using them some new characterizations are given for compactly packed lattices. Next, we study Noetherian lattices and Laskerian lattices and characterize Laskerian lattices in terms of compactly packed lattices.
We prove some optimal logarithmic estimates in the Hardy space ${H}^{\infty }(G)$ with Hölder regularity, where $G$ is the open unit disk or an annular domain of $\mathbb {C}$. These estimates extend the results established by S. Chaabane and I. Feki in the Hardy-Sobolev space $H^{k,\infty }$ of the unit disk and those of I. Feki in the case of an annular domain. The proofs are based on a variant of Hardy-Landau-Littlewood inequality for Hölder functions. As an application of these estimates, we study the stability of both the Cauchy problem for the Laplace operator and the Robin inverse problem.
We discuss the representability almost everywhere (a.e.) in C of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite number of isolated points. This brings us to the study of trajectories of the particular family of quadratic differentials A(z − a)(z − b)×(z − c)−2 dz2. More precisely, we give a necessary and sufficient condition on the complex numbers a and b for these quadratic differentials to have finite critical trajectories. We also discuss all possible configurations of critical graphs., Mohamed Jalel Atia, Faouzi Thabet., and Obsahuje seznam literatury