Bessel's Inequality

Bessel's Inequality states that for any function that can be broken down into a series of simpler, wave-like components (called Fourier series), the sum of the squares of the coefficients (which measure each component's contribution) is always less than or equal to the total amount of energy or information in the original function. Essentially, it guarantees that when approximating a function with these components, the sum of their individual impacts doesn’t exceed the original’s overall magnitude, ensuring a stable and consistent representation within the mathematical framework of orthogonal functions.