Introductory Functional Analysis with Applications — Kreyszig

Erwin Kreyszig (Wiley)

The standard first course in functional analysis: metric, normed, and Banach spaces; inner product and Hilbert spaces, orthogonality, and the projection theorem; the Hahn–Banach, uniform boundedness, open mapping, and closed graph theorems; and the spectral theory of bounded, compact, and self-adjoint operators. Deeper reading behind Course 1 Lessons 32, 36, 39, and 41 — metric spaces, signal space, transforms as operators, and dual spaces. For DSP this is the unifying frame: \(\ell^2\) and \(L^2\) are the signal spaces, orthonormal expansion is the Fourier transform, the projection theorem is least squares and Wiener filtering, and bounded operators are stable LTI systems.

Chapters

Exercises added as I work through each chapter.