An Introduction to Hilbert Space
by Nicholas Young · N. Young
Nicholas Young's undergraduate text develops inner product spaces, orthogonal expansions, and Fourier series, then turns to linear operators, Sturm-Liouville systems, and Hardy spaces. Readers finish able to apply Hilbert space methods to differential equations and approximation problems.
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More resources on Hilbert Spaces
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
nLab: Hilbert Space
Advanced reference with category theory perspective, linked in r/math discussions.