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| Volkmer H. — Multiparameter Eigenvalue Problems And Expansion Theorems |
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| Предметный указатель |
Accumulation points of eigenvalues 26 59
Arscott, F.M. 140
Atkinson, F.V. 20 49 74 77 86 113 114 140
Berman, A. 95
Binding, P. 20 48 49 74 75 86 113 114 140
Bocher, M. 74
Boundary eigenvalue problems 61
Boundary eigenvalue problems, definiteness conditions 65 66
Boundary eigenvalue problems, examples 4 68 72 135 136 138
Boundary eigenvalue problems, existence of eigenvalues 64 69 137
Boundary eigenvalue problems, expansion theorems 132 133 134 137 139
Boundary eigenvalue problems, oscillation theorems 64 67 137
Boundary eigenvalue problems, singular case 64 71
Boundedness principle 28 32 74
Boundedness principle, for left definite problems 99
Brouwer's degree of maps 8 12 14 74
Browne, P.J. 74 75 86 140
Carmichael, R.D. 20 113
Closable forms 51 52
Closure of forms 51 52 56
Coddington, E.A. 63
Continuity of eigenvalues 15 47 97
Coordinates, ellipsoidal 4 67 135 137 138
Coordinates, sphero-conal 139 140
Cordes, H.O. 140
Darai , A. 140
Decomposable eigenvector 76
Definiteness 17 42 60
Definiteness, criterion 85
Definiteness, left 43 60
Definiteness, local 8 21 39 57
Definiteness, local in the strong sense 22 39 59
Definiteness, right 42 60
Definiteness, strict left 61 66
Definiteness, strict right 61 66
Deimling, K. 13
Differential equations, Hamilton — Jacobi 62
Differential equations, Lame 67 70 71 72 138
Differential equations, Laplace 67
Differential equations, Mathieu 5
Differential equations, Schrodinger 137
Differential equations, wave equation 4 135
Differential operator, Laplace 137
Differential operator, ordinary 53 62 65
Differential operator, partial 4 128 134
Differential operator, uniformly elliptic 130 131 140
Discreteness of the spectrum 26
Dixon, A.C. 140 141
Dunford, N. 54
Eigencurve 2 3 98
Eigenspace 77 88 120
Eigensystem 90 101
Eigenvalue 8 21 50
Eigenvalue problems for bounded operators 21 87
Eigenvalue problems for bounded operators, approximation 87 90 113
Eigenvalue problems for bounded operators, continuity of eigenvalues 47 97
Eigenvalue problems for bounded operators, examples 38 107
Eigenvalue problems for bounded operators, existence of eigenvalues 36 43
Eigenvalue problems for bounded operators, expansion theorems 93 99 103 105
Eigenvalue problems for bounded operators, projection 25 90
Eigenvalue problems for bounded operators, uniqueness of eigenvalues 25
Eigenvalue problems for integral operators 107
Eigenvalue problems for integral operators, expansion theorems 109 112
Eigenvalue problems for matrices 8 76
Eigenvalue problems for matrices, completeness of eigenvectors 77 82 85
Eigenvalue problems for matrices, continuity of eigenvalues 15
Eigenvalue problems for matrices, examples 1 18
Eigenvalue problems for matrices, existence of eigenvalues 13
Eigenvalue problems for matrices, orthogonality of eigenvectors 79
Eigenvalue problems for matrices, uniqueness of eigenvalues 11
Eigenvalue problems for unbounded operators 50 116
Eigenvalue problems for unbounded operators, examples 61 64
Eigenvalue problems for unbounded operators, existence of eigenvalues 59
Eigenvalue problems for unbounded operators, expansion theorems 123 126 127 128
Eigenvalue problems for unbounded operators, transformation 56 116 120
Eigenvalue problems for unbounded operators, uniqueness of eigenvalues 59
Eigenvectors 78 89 121
Eigenvectors, decomposable 76
Ellipsoidal coordinates 4 67 135 137 138
Elliptic membrane 4
Erdelyi, A. 139
Existence of eigenvalues 13 36 43 59 64 137
Expansion theorems, in series of Lame products 139
Expansion theorems, in series of Lame's wave functions 137
Expansion theorems, preliminary 93 94
Expansion theorems, under definiteness 85
Expansion theorems, under left definiteness 99 112 123
Expansion theorems, under local definiteness 77 82
Expansion theorems, under right definiteness 103 105 109 126 127 134
Expansion theorems, under strict left definiteness 126 132
Expansion theorems, under strict right definiteness 128 133
Faierman, M. 74 75 140 141
Form determinants 77 78 88
Form determinants, positive definite 83
Form determinants, strictly definite 119
Fredholm integral operator 107
Gamma-operator 102 123
Garding's inequality 131
Hamilton — Jacobi equation 62
| Hausdorff, F. 49
Hilb, E. 74 141
Hilbert, D. 27 140
Howe, A. 75
Ince, E. 74
Index of eigenvalues 9 23 57
Jacobian elliptic functions 70 71
Jdrgens, K. 65 71
Joint range of forms 26
Kallstrom, A. 113 114 140
Kalnins, E.G. 4
Kato, T. 51 56 101
Klein's oscillation theorem 67 70
Klein, F. 67 70 74
Lame functions 73 140
Lame polynomials 70 71 73 138
Lame products 138 139 140 141
Lame's differential equation 67 70 71 72 73 138
Lame's differential equation, Jacobian -form 72 138
Lame's wave functions 116
Laplace equation 67
Laplace series 140
Left definiteness 43
Left definiteness, relations 44
Left definiteness, strict left 61 66
Levinson , N. 63
Limit-circle case 65 71
Limit-point case 65
Local definiteness 8 21 57
Local definiteness, criterion 16 24
Local definiteness, in the strong sense 22 59
Local definiteness, motivation 82
Local definiteness, relation to definiteness 17 18
Local definiteness, relation to local definiteness in the strong sense 40 60 65
Local definiteness, relation to other definiteness conditions 44
Magnus, W. 139
Mathieu's differential equation 5
Maximum-minimum principle 9 15 23 25 38 45 52
Meixner, J. 4 6 135 136 140
Miller, W., Jr 4
Minkowski matrices 87 94
Multiplication operator 62 65 128 132
Multiplicity of eigenvalues 9 23 57 63 76 78 80 89
Nagy 8 27
Oberhettinger, F. 139
Operator determinant 86 120 122 125 128
Orthogonality of eigenvectors 79 89
Oscillation theorem, abstract 37 74
Oscillation theorem, Klein's 67 70 74
Oscillation theorems 63 64 70 73 74 137
Pell, A. 49 114 115
Plenwions, R.J. 95
Reid, W.T. 54 55
Rellich, F. 65 71
Richardson, R.G. 74
Riesz, F. 27
Right definiteness 42 60
Right definiteness, relations 44
Right definiteness, strict right 61 66
Roach, G.F. 141
Sansone, G. 140
Schaefke, F.W. 4 6 135 136 140
Schaefke, R. 75
Schmidt, D. 136 138 140
Schroedinger equation 137
Schwartz, J.T. 54
Semibounded operators with compact resolvent 51 54 65
Separation constants 3 5 67 129 136
Separation of variables 3 5 62 67 116 128 129 130 135 138 140
Sequences of compact Hermitian operators 45 93
Signed index 11 24 57
Signed index, signum of eigenvalues 11 24 57
Sleeman, B.D. 74 113 114 140
Sobolev space 7 116 130 131 132
Spherical surface harmonics 139 140
Sphero-conal coordinates 139 140
Staeckel, P. 62
Stenger, W. 9
Stieltjes' theorem 71 73 138
Stieltjes, T.J. 71
Strict left definteness 61
Strict left definteness, criterion 65
Strict right definteness 61
Strict right definteness, criterion 65
Sturm — Liouville 6 50 54 63 64 65 74 75 140 141
Tensor product 76 88 108 117
Tensorial product 77 88 118 120
Tricomi, F.G. 139
Turyn, L. 75
Uniqueness of eigenvalues 11 25 59
Watson, G.N. 70
Wave equation 4 135 136
Weak topology 27 46
Weinstein, A. 9
Whittaker, E.T. 70
Wolf, G. 136 138 140
Yandermonde determinant 136
Yolkmer, H. 20 48 49 74 75 86 114 115 140 141
Yoshida, K. 130 131
Yoshikawa, J. 74
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