About equality of the cosine transform to the sine transform of Fourier   and the transform of Laplace
  Regularity of the transform of Laplace in the opened area of 0 is proved with help of some methods of the transform of Fourier. The class of the transform of Laplace from the transform of Fourier is considered from some functions without a regularity in null.   The functions are regular in the opened area of 0. 
Andrei V Pavlov-Maxorin
math.GM