31. This unitary extension of the Fourier transform is what we mean by the Fourier transform on the space of square integrable functions . 32. Indeed, there exists a unique series representation for a square integrable function " f " expressed in this basis: 33. This yields an action of the Poincare group on the space of square-integrable functions defined on the hypersurface in Minkowski space. 34. In formal terms, this representation is a wavelet series representation of a square-integrable function with respect to either a coherent states. 35. The space of all Henstock Kurzweil-integrable functions is often endowed with the Alexiewicz norm, with respect to which it is incomplete. 36. The Hilbert space may be taken to be the set of square integrable functions on the real number line ( the plane waves ). 37. This definition makes sense if " x " is an integrable function ( in distribution, or is a finite Borel measure. 38. Can anyone help me prove that the Fourier transform of an integrable function over "'R "'is uniformly continuous? 39. The Hilbertian tensor product of two copies of is isometrically and linearly isomorphic to the space of square-integrable functions on the square. 40. The convolution of any integrable function of period 2 with the Dirichlet kernel coincides with the function's th-degree Fourier approximation.
