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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

8 votes
1 answer
848 views

Basis vs Schauder basis in normed spaces

Following the conventions from Heil: "A Basis Theory Primer" and Albiac, Kalton: "Topics in Banach Space Theory", we might define a basis of an (infinite-dimensional) normed space $V$ as a sequence $( …
Ivica Smolić's user avatar
2 votes
1 answer
793 views

Proof of Helmholtz-Hodge decomposition, poor man's version

Helmholtz (-Hodge) decomposition commonly used in physics includes decomposition of a (sufficiently smooth) vector field $F = -\mathrm{grad}(U) + \mathrm{curl}(W)$ on bounded simply connected domain $ …
Ivica Smolić's user avatar