Supremum Norm — Topic Summaries
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Weierstrass M-Test
The Weierstrass M-test provides a clean, practical way to prove uniform convergence for series of functions. If a series of functions...
Real Analysis 25 | Uniform Convergence [dark version]
Uniform convergence is the stronger notion of convergence for functions where a single “eventually” index works for every point in the domain at...
Functional Analysis 14 | Example Operator Norm [dark version]
A linear functional built from a fixed continuous, zero-free function G on the unit interval has an operator norm equal exactly to the integral of...
Fourier Transform 14 | Uniform Convergence of Fourier Series
Fourier series typically converge in an L2 sense, meaning the “average squared error” over a period goes to zero, but point-by-point convergence is...