# What is “Applied Harmonic Analysis”?

Does it mean the application of the theorems of Harmonic Analysis to real-world problems, say, engineering or data science problems, and that Applied Harmonic Analysis is not about theory or proofs? And since it's "applied", does that mean there's no measure theory involved, except for the very minimal: monotone convergence and dominated convergence theorems?

• Ddi you check this? – user99914 Sep 17 '16 at 7:27
• – Watson Sep 17 '16 at 9:19
• See signal processing. Fourier analysis and hence distribution theory is used a lot, even if there is no need to be as rigorous as in pure maths. – reuns Sep 26 '17 at 12:41

These bases include wavelets, orthogonal polynomials, reproducing kernels, and others. To provide a rigorous analysis of these representations, often convergence results require that the estimated functions reside in some Hilbert space (most frequently) or Banach space (such as $$C[0,1]$$). For example, Representer Theorems lean on projections available in a Hilbert space to yield guarantees as to the structure of the solution to certain regularized optimization problems.