Index

Adjoint operator, 2

Algebraic multiplicity, 33

differential operator, 84, 86, 92-95, 98,

101

n even, 133, 134, 136, 146, 232, 238

n odd, 152, 155, 168, 181, 245

Fredholm operator, 48, 56-58

Ascent, 30, 31

differential operator, 84, 92, 98

n even, 133, 134, 136, 146, 232, 238

n odd, 152, 155, 168, 181, 245

Fredholm operator, 57-59

Ascent factor

Fredholm operator, 48, 54

Boundary coefficient matrix, 97, 211

Boundary values, 9, 83, 88, 97, 105, 109, 211

adjoint, 9, 83

degenerate, 98, 116, 118, 124

irregular, 87, 98, 111, 116, 119, 124, 128,

136, 146, 181

n even, 110-118

n odd, 118-128

normalized, 97, 117, 124, 211

order of, 97

regular, 87, 98, 111, 116, 119, 124, 128,

146, 181, 193, 201, 206, 212, 213, 225,

232, 239

B2{H), Hilbert-Schmidt operators, 64

Banach algebra, 65, 66

inner product, 66

Caratheodory's Inequality, 77

Carleman Inequality, 67, 68, 70, 74, 77, 80

finite-dimensional range, 71

finite-dimensions, 69

quasi-nilpotent Hilbert-Schmidt operator,

77, 78

Carleman theory, 64, 67

Cauchy domain, 14, 18, 36, 71

Cauchy Integral Formula, 15

Cauchy's Theorem, 14, 18, 20, 71, 86

Chain basis, 92-95

Characteristic determinant D, 86, 91 ,

92-95, 101, 102

order of zero, 92, 95

zero of, 91

Characteristic determinant A, 27, 98, 100,

101-102, 107, 117, 128, 133, 136, 140,

143, 146, 152, 155, 162, 168, 175, 193,

201, 212, 229-231, 237, 244

asymptotic formula, 98, 115, 122

n even, 100

n odd, 100

order of zero, 101

zero of, 98, 100, 102

Characteristic determinant Ao, 107, 108,

146, 148, 154, 157, 165, 171, 178, 201

asymptotic formula, 126

Closed Graph Theorem, 6, 21, 26, 32, 79

Closed linear operator, 6

examples, 7

reduced by pair of subspaces, 28

Closed Range Theorem, 8

Closure of an operator, 8

examples, 8

Cofactor, 106, 109, 116, 123, 127

Compact linear operator, 34

ascent and descent, 34

Completeness theorem, 64, 80, 185, 191, 217

Continuity of inversion, 19

Continuous spectrum, 21

Cramer's rule, 106, 109

Curve

closed, 13

rectifiable, 13

simple, 13

trace of, 13

Cycle

homologous to zero, 20

surrounds the spectrum, 20

Defect, 41, 48, 51, 52

Descent, 30, 31

Differential operator, 8, 83, 211

adjoint operator, 83

algebraic multiplicity, see Algebraic

multiplicity, differential operator

ascent, see Ascent, differential operator

basis for solution space, 91, 93, 94, 99,

101, 103, 107, 212

boundary coefficient matrix, see

Boundary coefficient matrix