On the dimension of graphs of Weierstrass-type functions with rapidly growing frequencies

We determine the Hausdorff and box dimension of the fractal graphs of some Weierstrass-type functions of the form (ProQuest: Formulae and/or non-USASCII text omitted), where g is a periodic Lipschitz real function and a sub()n1a sub()n arrow right 0, b sub()n1b sub()n arrow right [infinity] as n arrow right [infinity]. Moreover, for any 1 [< or =, slant] H [< or =, slant] B [< or =, slant] 2 we provide examples of such functions with dim sub()H(graph [functionof]) = dim sub(B)(graph [functionof]) = H, dim sub(B)(graph [functionof]) = B.