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