The object of the present paper
is to define a new type of contraction, called ‘Shrivel’, of a function and to prove a
theorem on the absolute convergence of its Fourier series. Our theorem is similar to a
theorem of M. Kinukawa, but as it is shown in the end the two results are essentially
different. The original results in this direction are due to A. Beurling and R. P.
Boas.