 This theorem states that the number of asymptotic values attained by an entire function of order ρ along curves in the complex plane going outwards toward infinite absolute value is less than or equal to 2ρ.In 1935, Torsten Carleman introduced a generalisation of Fourier transform, which foreshadowed the work of Mikio Sato on hyperfunctions; his notes were published in .He considered the functions "f" of at most polynomial growth, and showed that every such function can be decomposed as "f" = "f"+ + "f"−, where "f"+ and "f"− are analytic in the upper and lower half planes, respectively, and that this representation is essentially unique.