Pinsky Phenomenon
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High Quality Content by WIKIPEDIA articles! The Pinsky phenomenon is a result in Fourier analysis, a branch of mathematics. This phenomenon was discovered by Mark Pinsky of Northwestern University in Evanston, Illinois. It involves the spherical inversion of the Fourier transform. Suppose n = 3 and let the function g( x) = 1 for all x such that x c, with g( x ) = 0 elsewhere. This example demonstrates a phenomenon of Fourier inversion in three dimensions. The jump at x = c. causes an oscillatory behavior of the spherical partial sums, in particular a lack of convergence at the center of the ball:no possibility of Fourier inversion at x = 0.…mehr

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High Quality Content by WIKIPEDIA articles! The Pinsky phenomenon is a result in Fourier analysis, a branch of mathematics. This phenomenon was discovered by Mark Pinsky of Northwestern University in Evanston, Illinois. It involves the spherical inversion of the Fourier transform. Suppose n = 3 and let the function g( x) = 1 for all x such that x c, with g( x ) = 0 elsewhere. This example demonstrates a phenomenon of Fourier inversion in three dimensions. The jump at x = c. causes an oscillatory behavior of the spherical partial sums, in particular a lack of convergence at the center of the ball:no possibility of Fourier inversion at x = 0.