منابع مشابه
A Note on the Convolution Theorem for the Fourier Transform
In this paper we characterize those bounded linear transformations Tf carrying L1(R1) into the space of bounded continuous functions on R1 , for which the convolution identity T (f ∗ g) = Tf ·Tg holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.
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We present a new inversion formula for the classical, finite, and asymptotic Laplace transform f̂ of continuous or generalized functions f . The inversion is given as a limit of a sequence of finite linear combinations of exponential functions whose construction requires only the values of f̂ evaluated on a Müntz set of real numbers. The inversion sequence converges in the strongest possible sens...
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We review the Fourier-Laguerre transform, an alternative harmonic analysis on the three-dimensional ball to the usual Fourier-Bessel transform. The Fourier-Laguerre transform exhibits an exact quadrature rule and thus leads to a sampling theorem on the ball. We study the definition of convolution on the ball in this context, showing explicitly how translation on the radial line may be viewed as...
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A new linear transform is deened for real valued functions which can be expanded in Taylor series. For an image which can be expressed by the Taylor expansion of a function, the new transform corresponds to convolution of the image with a point spread function. The point spread function must satisfy the condition that it's zero-th moment is non-zero and positive integer moments are nite. The fo...
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ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 1959
ISSN: 0386-5991
DOI: 10.2996/kmj/1138844136