How to do the Fourier Transform of bounded function?

1. Is the Fourier transform bounded?
2. What is the Fourier transform of a function?
3. What is the Fourier transform of Dirac function?
4. What is the formula for Fourier transform?

Is the Fourier transform bounded?

It is true that Fourier transform is not a bounded operator from Lp(R) to Lq(R) (1/p+1/q=1) when p>2.

What is the Fourier transform of a function?

The Fourier transform is a mathematical function that decomposes a waveform, which is a function of time, into the frequencies that make it up. The result produced by the Fourier transform is a complex valued function of frequency.

What is the Fourier transform of Dirac function?

The Fourier transform of a function (for example, a function of time or space) provides a way to analyse the function in terms of its sinusoidal components of different wavelengths. The function itself is a sum of such components. The Dirac delta function is a highly localized function which is zero almost everywhere.

What is the formula for Fourier transform?

As T→∞, 1/T=ω0/2π. Since ω₀ is very small (as T gets large, replace it by the quantity dω). As before, we write ω=nω0 and X(ω)=Tc_n. A little work (and replacing the sum by an integral) yields the synthesis equation of the Fourier Transform.