This covers all transformations of functions by integrals, including but not limited to the Radon, X-Ray, Hilbert, Mellin transforms. Use (wavelet-transform), (laplace-transform) for those respective transforms, and use (fourier-analysis) for questions about the Fourier and Fourier-sine/cosine ...

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116 views

When to use the Functional Determinant in Polar Coordinate Transformation

I am currently learning about polar coordinate transformation, especially for integrating over certain regions. Let's say we have to calculate $\int_{n}{xy \; dx dy}$ Then I think the correct ...
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1answer
2k views

Does a Fourier transformation on a (pseudo-)Riemannian manifold make sense?

the Fourier transformation of a scalar function with respect to one variable might be defined as $\mathcal{F}\left[w\right](\omega )\equiv ...
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4answers
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Connection between Fourier transform and Taylor series

Both Fourier transform and Taylor series are means to represent functions in a different form. My question: What is the connection between these two? Is there a way to get from one to the other (and ...
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7answers
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Laplace transformations for dummies

Is there a simple explanation of what the Laplace transformation do exactly and how they work? Reading my math book has left me in a foggy haze of proofs that I don't completely understand. I'm ...
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973 views

Inverse of Laplace transform

There is a very simple expression for the inverse of Fourier transform. What is the easiest known expression for the inverse Laplace transform? Moreover, what is the easiest way to prove it?