Adams inequality on the hyperbolic space

J Rgensen's Inequality for Complex Hyperbolic Space

Jørgensen’s inequality for quaternionic hyperbolic n-space

Jørgensen’s inequality gives a necessary condition for a non-elementary two generator group of isometries of real hyperbolic 2-space to be discrete. We give analogues of Jørgensen’s inequality for non-elementary groups of isometries of quaternionic hyperbolic n-space generated by two elements, one of which is loxodromic. Mathematics Subject Classifications (2000): 20H10, 22E40, 57S30.

Jørgensen’s inequality for quternionic hyperbolic space with elliptic elements

In this paper, we give an analogue of Jørgensen’s inequality for non-elementary groups of isometries of quaternionic hyperbolic space generated by two elements, one of which is elliptic. As an application, we obtain an analogue of Jørgensen’s inequality in 2-dimensional Möbius group of the above case. 2000 Mathematics subject classification: primary 30F40; secondary 20H10, 57S30.

Jørgensen’s Inequality and Collars in n-dimensional Quaternionic Hyperbolic Space

In this paper, we obtain analogues of Jørgensen’s inequality for non-elementary groups of isometries of quaternionic hyperbolic n-space generated by two elements, one of which is loxodromic. Our result gives some improvement over earlier results of Kim [10] and Markham [15]. These results also apply to complex hyperbolic space and give improvements on results of Jiang, Kamiya and Parker [7]. As...

Universal Approximator Property of the Space of Hyperbolic Tangent Functions

In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.