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Dependency graph
1
The problem and the result
2
Matrices and operators in the Loewner order
▶
2.1
Comparison with multiples of the identity
2.2
Traces of products
2.3
The trace of a positive operator
2.4
From the trace of an inverse to the Loewner order
2.5
Rank-one updates
3
Averages of quadratic forms
▶
3.1
The Gram matrix
3.2
The Gram operator
3.3
A reproducing kernel Hilbert space
3.4
A point from two averages
4
The lower potential and its barrier
▶
4.1
The potential and the verifier
4.2
The verifier passes on average
4.3
From the potential to the frame bound
5
The upper potential and its barrier
▶
5.1
The upper potential and the verifier
5.2
The upper verifier passes on average
5.3
From the upper potential to the frame bound
6
The construction and the proof
▶
6.1
The barrier iteration
6.2
Proof of the discretization theorem
7
Discretization of the uniform norm and the \(L_p\)-norms
▶
7.1
The proof of the Kiefer–Wolfowitz theorem
References
Blueprint: Norm Discretization
Mario Ullrich
GitHub:
Lean-Discretization
Dependency graph
1
The problem and the result
2
Matrices and operators in the Loewner order
2.1
Comparison with multiples of the identity
2.2
Traces of products
2.3
The trace of a positive operator
2.4
From the trace of an inverse to the Loewner order
2.5
Rank-one updates
3
Averages of quadratic forms
3.1
The Gram matrix
3.2
The Gram operator
3.3
A reproducing kernel Hilbert space
3.4
A point from two averages
4
The lower potential and its barrier
4.1
The potential and the verifier
4.2
The verifier passes on average
4.3
From the potential to the frame bound
5
The upper potential and its barrier
5.1
The upper potential and the verifier
5.2
The upper verifier passes on average
5.3
From the upper potential to the frame bound
6
The construction and the proof
6.1
The barrier iteration
6.2
Proof of the discretization theorem
7
Discretization of the uniform norm and the \(L_p\)-norms
7.1
The proof of the Kiefer–Wolfowitz theorem
References