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My take is : "If you use the third definition, the inverse transform will have $\sqrt\frac{1}{2\pi}$ factor and will be very similar to the direct transform)." (lifted from answer there). I'd like to …

Quart. J. Math. Volume 37, Issue 1, Pages 53-79 On double Fourier series, and especially those which represent the double zeta-function with real and incommensurable parameters. Hardy, G.H. I am not …

I am retreating back on this statement, after some explorations and calculation Bow to Willie and others who were skeptical on this. Main difficulty can be seen in this reference. But I must mention t …

I would like to prove for the case of jump discontinuity of the function itself. (rather than that of one of its derivatives). Let $t_0>0$ be a point where $f$ jumps. The curve $$(X_{t_0}(s),Y_{t_0}( …

For a real valued function $f(t)$ I want to check the information left, after taking a Fourier partial sum/integral. Let $\hat{f}$ be its Fourier transform and let $$e_{\omega}(t) = f(t) - \int\limits …

I am working on a problem, which would possibly relate the Fourier transform/series with the jump singularities of the function where the function itself or one of its derivatives jump. ((some kind of …