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Words: 3k
Articles: 107
Table of contents
3k
107
Integral operator
Functional analysis
31
Normed vector space
Functional analysis
249
10
L1 norm
Normed vector space
10
Euclidean norm
Normed vector space
32
1
Euclidean ball
Euclidean norm
23
Supremum norm
Normed vector space
28
Surjective isometry of normed vector spaces
Normed vector space
120
3
Mazur-Ulam theorem
Surjective isometry of normed vector spaces
78
1
Metric extraction of a midpoint by shrinking diameters
Mazur-Ulam theorem
59
Nonsurjective isometry need not preserve midpoints
Surjective isometry of normed vector spaces
29
Banach space
Normed vector space
40
1
Uniform boundedness principle
Banach space
25
Stone-Weierstrass theorem
Functional analysis
85
2
Weierstrass approximation theorem
Stone-Weierstrass theorem
45
1
Bernstein polynomial
Weierstrass approximation theorem
33
Open mapping theorem (functional analysis)
Functional analysis
48
1
Bounded inverse theorem
Open mapping theorem
21
Diagonal operator on sequence space
Functional analysis
58
1
Unbounded inverse on a nonclosed operator range
Diagonal operator on sequence space
23
Graph of a linear operator
Functional analysis
173
5
Closed graph theorem
Graph of a linear operator
158
4
Closed graph theorem from the bounded inverse theorem
Closed graph theorem
26
Closed-graph proof for a factored operator
Closed graph theorem
25
Incomplete-domain counterexample to closed-graph factorization
Closed graph theorem
24
Continuity of a positive linear map into a dual space
Closed graph theorem
67
Closed-range criterion for an injection
Functional analysis
25
Neumann-series perturbation
Functional analysis
22
Density by annihilators
Functional analysis
19
Hilbert space
Functional analysis
556
21
Closest point theorem in a Hilbert space
Hilbert space
77
1
Orthogonal decomposition by a closed subspace
Closest point theorem in a Hilbert space
35
Riesz representation theorem
Hilbert space
162
5
Adjoint operator
Riesz representation theorem
144
4
Hermitian operator
Adjoint operator
10
Adjoint criterion for an invariant orthogonal complement
Adjoint operator
28
Normal operator
Adjoint operator
66
1
Spectral theorem for normal operators
Normal operator
37
Weak convergence in a Hilbert space
Hilbert space
237
8
Coordinate criterion for weak convergence in a separable Hilbert space
Weak convergence in a Hilbert space
26
Weak subsequence of a bounded Hilbert-space sequence
Weak convergence in a Hilbert space
32
Weak lower semicontinuity of the Hilbert norm
Weak convergence in a Hilbert space
29
Radon-Riesz theorem
Weak convergence in a Hilbert space
58
1
Uniform basis-tail criterion for strong convergence
Radon-Riesz theorem
39
Weakly null orthonormal sequence
Weak convergence in a Hilbert space
23
Mazur lemma
Weak convergence in a Hilbert space
25
Norm-closed convex set is weakly closed
Weak convergence in a Hilbert space
26
Orthonormal sequence
Hilbert space
72
3
Hilbertian basis
Orthonormal sequence
46
1
Parseval identity for a Hilbertian basis
Hilbertian basis
15
Bessel inequality
Orthonormal sequence
12
Compact operator
Functional analysis
137
5
Hilbert-Schmidt operator
Compact operator
23
Finite-rank operator
Compact operator
9
Spectral theorem for compact Hermitian operators
Compact operator
51
1
Finite-rank truncation of a compact Hermitian operator
Spectral theorem for compact Hermitian operators
20
Coordinate-projection approximation of a compact operator
Compact operator
38
Sublinear functional
Functional analysis
15
Hahn-Banach theorem
Functional analysis
147
3
Canonical embedding into the bidual
Hahn-Banach theorem
40
Singular functional on L infinity
Hahn-Banach theorem
58
Hahn-Banach separation theorem
Hahn-Banach theorem
27
Banach-Alaoglu theorem
Functional analysis
15
Lax-Milgram theorem
Functional analysis
92
2
Weak Dirichlet problem for the massive Laplacian
Lax-Milgram theorem
57
1
Compact massive-Laplacian resolvent
Weak Dirichlet problem for the massive Laplacian
27
Sobolev space
Functional analysis
555
21
Sobolev derivative estimate
Sobolev space
19
Massive Laplacian isomorphism on Sobolev spaces
Sobolev space
20
Compactness from bounded support and an H2 bound
Sobolev space
34
Sobolev trace theorem
Sobolev space
70
1
Failure of an Lp hyperplane trace
Sobolev trace theorem
32
Regularity gain for one plus an even power of the Laplacian
Sobolev space
23
Sobolev embedding theorem
Sobolev space
338
13
Rellich-Kondrashov compactness theorem for H01
Sobolev embedding theorem
196
7
Zero extension of H01
Rellich-Kondrashov compactness theorem for H01
27
High-frequency control by a Sobolev derivative
Rellich-Kondrashov compactness theorem for H01
12
Fourier proof of Rellich compactness
Rellich-Kondrashov compactness theorem for H01
28
Weak lower semicontinuity of a bounded-domain Schrodinger energy
Rellich-Kondrashov compactness theorem for H01
69
1
Constrained ground-state minimizer on a bounded domain
Weak lower semicontinuity of a bounded-domain Schrodinger energy
35
Local compactness plus uniform tail control
Rellich-Kondrashov compactness theorem for H01
47
1
Strong convergence from weak convergence and tightness
Local compactness plus uniform tail control
27
Noncompactness of a Sobolev embedding by translation
Sobolev embedding theorem
92
2
Loss of compactness at infinity
Noncompactness of a Sobolev embedding by translation
25
Vanishing Dirichlet energy by dilation on the line
Noncompactness of a Sobolev embedding by translation
35
Hölder space
Sobolev embedding theorem
38
1
Fourier proof of Hölder regularity from a Sobolev norm
Hölder space
28
Ladyzhenskaya inequality in two dimensions
Sobolev space
30
Space of continuous functions vanishing at infinity
Functional analysis
83
2
Completeness of continuous functions vanishing at infinity
Space of continuous functions vanishing at infinity
49
Uniform square-root perturbation under linear growth
Space of continuous functions vanishing at infinity
21
Noncompactness by separated translates
Functional analysis
19
Continuous dual space
Functional analysis
195
7
Positive linear functional
Continuous dual space
26
Operator norm
Continuous dual space
35
1
Matrix 2-norm
Operator norm
26
Completeness of the dual space
Continuous dual space
28
Duality of sequence spaces
Continuous dual space
12
Duality of Lp spaces
Continuous dual space
78
1
Positive functional representation on Lp
Duality of Lp spaces
47
Holder inequality
Functional analysis
76
3
Conjugate exponents
Holder inequality
12
Norming vector for Holder inequality
Holder inequality
15
Minkowski integral inequality
Holder inequality
34
Space of sequences converging to zero
Functional analysis
42
2
Convergent sequence space
Space of sequences converging to zero
27
1
Absorption of a finite-dimensional summand by c0
Convergent sequence space
15
Banach space isomorphism
Functional analysis
12
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Analysis
Area of mathematics
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