Fourier Transforms in Two or More Variables
Part of the Applied Mathematical Sciences book series (AMS, volume 25)
The theory of Fourier transforms of a single variable may be extended to functions of several variables. Thus, if f(x,y) is a function of two variables, the function F(ξ, η) defined byis the two-dimensional Fourier transform of f(x,y), and, provided that the inversion formula (7.6) may be applied twice, we have.
KeywordsFourier Transform Radiation Condition Simple Algebra Fresnel Diffraction Fraunhofer Diffraction
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- 4.This result is given in I. N. Sneddon, J. Eng. Math. (1974), 8, 177, together with a discussion of the connection with the half-space Dirichlet problem for Laplace’s equation.Google Scholar
- 6.See DITKIN & PRUDNIKOV (1970) for more information on double Laplace transforms.Google Scholar
- 9.The application of the double Laplace transform to a more general second-order partial differential equation in the quadrant x 2265; 0, y 2265; 0 is discussed in K. Evans and E. A. Jackson, J. Math. Phys. (1971), 12, 2012.Google Scholar
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