Measure theoretic trigonometric functions

Discrete Trigonometric Matrix Functions

We explore a pair of matrix solutions to a certain discrete system which has various properties similar to the familiar continuous trigonometric functions, including basic identities and sum and difference of two angles formulas. Then we examine separation properties of these matrices. An oscillation result is also given.

Generalized Trigonometric Functions: 10744

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Measure-Theoretic Properties of Level Sets of Distance Functions

We consider the level sets of distance functions from the point of view of geometric measure theory. This lays the foundation for further research that can be applied, among other uses, to the derivation of a shape calculus based on the level-set method. Particular focus is put on the (n − 1)-dimensional Hausdorff measure of these level sets. We show that, starting from a bounded set, all sub-l...

Inequalities Involving Hyperbolic Functions and Trigonometric Functions

Inequalities involving hyperbolic functions and trigonometric functions are established. Most of the established inequalities can be regarded as the companion inequalities to those obtained by Lazarević, Adamović and Mitrinović and Cusa and Huygens The established results are obtained with the aid of the Schwab-Borchardt mean.

Trigonometric functions, elliptic functions, elliptic modular forms