On singular Sturm theorems
The article summarizes some developments about a singular versions of the Sturm Comparison and Separation theorems where the coefficients or the interval of definition may be unbounded.
math.CA↗
arXiv subjects
U. Elias
Publications and source records attributed to U. Elias.
More Jordan type inequalities
The function $ \tan(πx / 2) / (πx / 2) $ is expanded into a Laurent series of $ 1 - x^2 $, where the coefficients are given explicitly as combinations of zeta function of even integers. This is used to achieve a sequence of upper and lower bounds which are very precise even at the poles $ x = 1, -1 $. Similar results are obtained for other trigonometric functions with poles.
math.CA↗
Sufficient conditions for univalence of analytic functions
The article discusses criteria for univalence of analytic functions in the unit disc. Various families of analytic functions depending on real parameters are considered. A unified method for creating new sets of conditions ensuring univalence is presented. Applying this method we are able to find several families of new sharp criteria for univalence.
math.CV↗