Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators

Index

1. auto-covariance
   1. function
   2. operator

 

1. Banach Inverse Theorem
2. Banach-Alaoglu Theorem
3. basis
4. best linear predictor
5. bijective mapping
6. BLUP, 6, see best linear predictor
7. Bochner integral
8. Borel σ-field
9. bounded linear transformation
10. bounded variation
11. Brownian motion

 

1. canonical correlations
2. canonical variables
3. canonical weight vectors
4. Cauchy sequence
5. Cauchy's integral formula
6. closed linear span
7. closed set
8. closure
9. coefficient function
10. compact
11. complete orthonormal system
12. congruence relationship
13. CONS, see complete orthonormal system
14. continuous function
15. Courant-Fischer minimax principle
16. covariance
    1. function
    2. kernel
    3. matrix
    4. operator
17. cross validation
    1. generalized
    2. ordinary
18. cross-covariance
    1. function
    2. matrix
    3. operator

 

1. dense set
2. densely defined operator
3. dimension
4. direct product
5. direct sum
   1. algebraic
   2. orthogonal
6. discriminant analysis
7. domain
8. dual space

 

1. Eckart-Young Theorem
2. eigenfunction
3. eigenspace
4. eigenvalues
   1. non-repeated
   2. of a linear operator
   3. of a matrix
   4. repeated
5. evaluation functional
6. extension principle

 

1. factor loadings
2. factors
3. flat concentration
4. Fourier coefficients
5. Fréchet derivative

 

1. Gâteaux derivative
2. Gram-Schmidt algorithm

 

1. Hahn-Banach Extension Theorem
2. Heine-Borel Theorem
3. Hilbert-Schmidt inner product
4. HS operator, see Hilbert Schmidt operator

 

1. identity mapping
2. image
3. inequality
   1. Besssel
   2. Cauchy-Schwarz
   3. Hölder
   4. Minkowski
   5. triangle
   6. Young's
4. inner product
5. isometrically isomorphic

 

1. Karhunen-Lòeve Theorem
2. kernel of an operator

 

1. linear functional
2. linear ...