This paper develops a method for constructing rational parameterizations of knots, based on a trigonometric parameterization. It also introduces the class of torus knots and describes a method for constructing trigonometric and rational parameterizations of these knots. This research was conducted at the Mt. Holyoke REU, and was funded by the NSF through grant number DMS-9732228.

Five uniqueness questions for multiple trigonometric series are surveyed. If a multiple trigonometric series converges everywhere to zero in the sense of spherical convergence, of unrestricted rectangular convergence, or of iterated convergence, then that series must have every coefficient being zero. But the cases of square convergence and restricted rectangular convergence lead to open questi...

In this paper some inequalities for Dirichlet’s and Fejer’s kernels proved in [6] are refined and extended. Then we have obtained the conditions for L-convergence of the r-th derivatives of complex trigonometric series. These results are extensions of corresponding Bhatia’s and Ram’s results for complex trigonometric series (case r = 0).

In this paper we show that any symplectic difference system can be transformed into a trigonometric system, using a transformation that preserves oscillatory properties. Necessary and sufficient conditions for nonoscillation of a certain class of trigonometric systems are given, and this result is applied to oscillation theory of Hamiltonian difference systems. 2000 Academic Press