Index

Abel transform, 5

Abel's map, 281

Abel's theorem, 282

Abelian differentials, 275

Additive process, 91

Almost Mathieu operator, 101

Almost periodic sequence, 100

Anderson model, 88

Antisymmetric part, 15

Asymptotic expansion, 106

Backlund transformation, 259

Baker-Akhiezer function, 148

Banach space, 3

Bessel function, 25

Birkhoff's ergodic theorem, 91

Birman-Schwinger type bound, 70

Borel

measure, 297

set, 297

transform, 298

Boundary condition, 16, 18

Branch number, 274

Burchnall-Chaundy polynomial, 234

Canonical divisor, see divisor

Canonical form, 40

Canonical homology basis, 274

Casoratian, 189

Cauchy

transform, 298

Characteristic polynomial, 12

Closure

essential, 301

operator, 47

Commutation method, 185

Dirichlet deformation method, 207

double, 198

single, 187

Commutator, 224

Conservation law, 252

Continued fraction, 10

Crystal

exponential interaction, 221

linear interaction (harmonic), 22

C* -algebra, 227

Cyclic vector, 40

Deficiency indices, 48

Degree, 274

Degree of a divisor, see divisor

Density of states, 95

Deterministic sequences, 100

Difference expression, 4

commuting, 231

matrix representation, 4

order, 4

second order, symmetric, 5

skew-symmetric, 4

symmetric, 4

triangular parts, 5

Dirac operator, 262

Dirichlet boundary condition, 16

Dirichlet eigenvalues, 134

Discriminant, 116

Dispersion, 25

relation, 25

Divisor, 277

associated with eigenvalues, 154

canonical, 278

degree, 277

index of specialty, 279

nonspecial, 279

positive, 279

principal, 278

relatively prime, 279

Divisor class group, 278

Divisor of poles, 279

Divisor of zeros, 279

Double commutation method, 198

Dynamical system, 87

ergodic, 88

Eigenfunction expansion, 40, 45

Elliptic functions, 162

Elliptic integral, 163

Ergodic, 88

Essential spectrum, 60