Linear maps between function spaces by integration against a kernel — Fourier, Laplace, Mellin, Hankel, wavelet. Diagonalise translation, exponential decay, scaling, and rotational symmetries respectively; turn PDEs into algebraic problems.
Linear maps between function spaces by integration against a kernel — Fourier, Laplace, Mellin, Hankel, wavelet. Diagonalise translation, exponential decay, scaling, and rotational symmetries respectively; turn PDEs into algebraic problems.