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Analysis
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B
Basic real analysis
C
Complex analysis
D
Differential equations
F
Fourier analysis
Functional analysis
H
Harmonic analysis
P
Partial differential equations
R
Real analysis
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F
Functional analysis front page
I
I have a problem about open or closed sets
L
Lower degree by increasing dimension (or vice-versa)
O
Order by property
T
To construct a function with several local constraints, start with simple cases and build from there
To construct exotic sets, use limiting arguments
To make a function less variable without changing it much, compare it with less variable functions
To prove that a set is open or closed, use basic theorems rather than direct arguments
To represent one object as combinations of another, try averaging the latter object using the symmetries of the former
U
Use conservation laws and monotonicity formulae to obtain long-time control on solutions
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