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
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