Hilbert Space, boundary value problems and orthogonal polynomials:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2002
|
| Series: | Operator theory
133 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 352 S.: 24 cm |
| ISBN: | 3764367016 |
Staff View
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| 100 | 1 | |a Krall, Allan M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Hilbert Space, boundary value problems and orthogonal polynomials |c Allan M. Krall |
| 246 | 1 | 3 | |a Problems and orthogonal polynomials |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2002 | |
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| 650 | 4 | |a Orthogonal polynomials | |
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Record in the Search Index
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|---|---|
| adam_text | IMAGE 1
HUBERT SPACE,
BOUNDARY VALUE PROBLEMS AND ORTHOGONAL POLYNOMIALS
ALLAN M. KRALL
BIRKHAEUSER VERLAG BASEL * BOSTON * BERLIN
IMAGE 2
CONTENTS
PREFACE XIII
PART 1
I HUBERT SPACES 1 LINEAR SPACES 1
2 HERMITIAN FORMS 3
3 HUBERT SPACES 6
4 PROJECTIONS 9
5 CONTINUOUS LINEAR FUNCTIONALS 12
6 ORTHONORMAL SETS 13
7 ISOMETRIC HUBERT SPACES 15
II BOUNDED LINEAR OPERATORS ON A HUBERT SPACE
1 BOUNDED LINEAR OPERATORS 17
2 THE ADJOINT OPERATOR 19
3 PROJECTIONS 21
4 SOME SPECTRAL THEOREMS 23
5 OPERATOR CONVERGENCE 28
6 THE SPECTRAL RESOLUTION OF A BOUNDED SEIF-ADJOINT OPERATOR 33
7 THE SPECTRAL RESOLUTION OF BOUNDED NORMAL AND UNITARY OPERATORS 37
7.1 NORMAL OPERATORS 37
7.1 UNITARY OPERATORS 39
III UNBOUNDED LINEAR OPERATORS ON A HUBERT SPACE
1 UNBOUNDED LINEAR OPERATORS 41
2 THE GRAPH OF AN OPERATOR 42
3 SYMMETRIE AND SEIF-ADJOINT OPERATORS 44
4 THE SPECTRAL RESOLUTION OF AN UNBOUNDED SEIF-ADJOINT OPERATOR 46
IMAGE 3
VIII CONTENTS
PART 2
IV REGULAER LINEAR HAMILTONIAN SYSTEMS 1 THE REPRESENTATION OF SCALAR
PROBLEMS 51
2 DIRAC SYSTEMS 54
3 S -HERMITIAN SYSTEMS 56
4 REGULAER LINEAR HAMILTONIAN SYSTEMS 57
5 THE SPECTRAL RESOLUTION OF A REGULAER LINEAR HAMILTONIAN OPERATOR 64
6 EXAMPLES 70
V ATKINSON S THEORY FOR SINGULAR HAMILTONIAN SYSTEMS OF EVEN DIMENSION
1 SINGULAR HAMILTONIAN SYSTEMS 74
2 EXISTENCE OF SOLUTIONS IN L 2 A (A, B) 75
3 BOUNDARY CONDITIONS 79
4 A PRELIMINARY GREENS FORMULA 81
VI THE NIESSEN APPROACH TO SINGULAR HAMILTONIAN SYSTEMS
1 BOUNDARY VALUES OF HERMITIAN FORMS 88
2 THE EIGENVALUES OF A(X) 91
3 GENERALIZATION OF THE SECOND WEYL THEOREM 92
4 SINGULAR BOUNDARY VALUE PROBLEMS 94
5 THE GREEN S FUNCTION 95
6 SELF-ADJOINTNESS 97
7 MODIFIKATION OF THE BOUNDARY CONDITIONS 100
8 OTHER BOUNDARY CONDITIONS 102
9 THE LIMIT POINT CASE 102
10 THE LIMIT M CASE 103
11 THE LIMIT CIRCLE CASE 104
12 COMMENTS CONCERNING THE SPECTRAL RESOLUTION 106
VII HINTON AND SHAW S EXTENSION OF WEYL S M(X) THEORY TO SYSTEMS
1 NOTATIONS AND DEFINITIONS 107
2 THE M(A) MATRIX 109
3 M CIRCLES 111
4 SQUARE INTEGRABLE SOLUTIONS 115
5 SINGULAR BOUNDARY CONDITIONS 117
6 THE DIFFERENTIAL OPERATOR L 118
7 EXTENSION OF THE BOUNDARY CONDITIONS 122
8 THE EXTENDED GREEN S FORMULA WITH ONE SINGULAR POINT 125
IMAGE 4
CONTENTS IX
9 SELF-ADJOINT BOUNDARY VALUE PROBLEMS WITH MIXED BOUNDARY CONDITIONS
131
10 EXAMPLES 132
VIII HINTON AND SHAW S EXTENSION WITH TWO SINGULAR POINTS
1 M{ ) FUNCTIONS, LIMIT CIRCLES, L 2 SOLUTIONS 138
2 THE DIFFERENTIAL OPERATOR 141
3 THE RESOLVENT, THE GREEN S FUNCTION 142
4 PARAMETER INDEPENDENCE OF THE DOMAIN 144
5 THE EXTENDED GREEN S FORMULA WITH TWO SINGULAR POINTS 145
6 EXAMPLES 148
6.1 THE JACOBI BOUNDARY VALUE PROBLEM 149
6.2 THE LEGENDRE BOUNDARY VALUE PROBLEM 150
6.3 THE TCHEBYCHEFF PROBLEM OF THE FIRST KIND 150
6.4 THE TCHEBYCHEFF PROBLEM OF THE SECOND KIND 151
6.5 THE GENERALIZED LAGUERRE BOUNDARY VALUE PROBLEM 152
6.6 THE ORDINARY LAGUERRE BOUNDARY VALUE PROBLEM 152
6.7 THE HERMITE BOUNDARY VALUE PROBLEM 152
6.8 BESSEL FUNCTIONS 153
6.9 THE LEGENDRE SQUARED PROBLEM 154
6.10 THE LAGUERRE-TYPE PROBLEM 155
IX THE M( ) SURFACE
1 THE CONNECTION BETWEEN THE HINTON-SHAW AND NIESSEN APPROACHES 159
2 A DIRECT APPROACH TO THE M{ ) SURFACE 162
3 EXAMPLES 164
X THE SPECTRAL RESOLUTION FOR LINEAR HAMILTONIAN SYSTEMS WITH ONE
SINGULAR POINT
1 THE SPECIFIC PROBLEM 167
2 THE SPECTRAL EXPANSION 168
3 THE CONVERSE PROBLEM 176
4 THE RELATION BETWEEN M{ ) AND P( ) 181
5 THE SPECTRAL RESOLUTION 182
6 AN EXAMPLE 184
7 SUBSPACE EXPANSIONS 185
8 REMARKS 187
IMAGE 5
X CONTENTS
XI THE SPECTRAL RESOLUTION FOR LINEAR HAMILTONIAN SYSTEMS WITH TWO
SINGULAR POINTS
1 THE SPECIFIC PROBLEM 189
2 THE SPECTRAL EXPANSION 190
3 THE CONVERSE PROBLEM 199
4 THE RELATION BETWEEN M A , M B , AND P(X) 203
5 THE SPECTRAL RESOLUTION 205
XII DISTRIBUTIONS
1 TEST FUNCTIONS WITH COMPACT SUPPORT, D; DISTRIBUTIONS WITHOUT
CONSTRAINT, D 1 207
2 LIMITS OF DISTRIBUTIONS 211
3 TEST FUNCTIONS OF RAPID DECAY, 5; DISTRIBUTIONS OF SLOW GROWTH, S 212
4 TEST FUNCTIONS OF SLOW GROWTH, P; DISTRIBUTIONS OF RAPID DECAY, P 213
5 TEST FUNCTIONS WITHOUT CONSTANTS, E; DISTRIBUTIONS OF COMPACT SUPPORT,
E 214
6 DISTRIBUTIONAL DIFFERENTIAL EQUATIONS 215
PART 3
XIII ORTHOGONAL POLYNOMIALS 1 BASIC PROPERTIES OF ORTHOGONAL POLYNOMIALS
223
2 ORTHOGONAL POLYNOMIALS, DIFFERENTIAL EQUATIONS, SYMMETRY FACTORS AND
MOMENTS 226
XIV ORTHOGONAL POLYNOMIALS SATISFYING SECOND ORDER DIFFERENTIAL
EQUATIONS
1 THE GENERAL THEORY 237
2 THE JACOBI POLYNOMIALS 239
3 THE LEGENDRE POLYNOMIALS 243
4 THE GENERALIZED LAGUERRE POLYNOMIALS 245
5 THE HERMITE POLYNOMIALS 249
6 THE GENERALIZED HERMITE POLYNOMIALS 252
6.1 THE GENERALIZED HERMITE POLYNOMIALS OF EVEN DEGREE 253
6.2 THE GENERALIZED HERMITE POLYNOMIALS OF ODD DEGREE 255
7 THE BESSEL POLYNOMIALS 257
IMAGE 6
CONTENTS XI
XV ORTHOGONAL POLYNOMIALS SATISFYING FOURTH ORDER DIFFERENTIAL EQUATIONS
1 THE GENERAL THEORY 261
2 THE JACOBI POLYNOMIALS 262
3 THE GENERALIZED LAGUERRE POLYNOMIALS 264
4 THE HERMITE POLYNOMIALS 265
5 THE LEGENDRE-TYPE POLYNOMIALS 265
6 THE LAGUERRE-TYPE POLYNOMIALS 270
7 THE JACOBI-TYPE POLYNOMIALS 274
XVI ORTHOGONAL POLYNOMIALS SATISFYING SIXTH ORDER DIFFERENTIAL EQUATIONS
1 THE H.L. KRALL POLYNOMIALS 281
2 THE LITTLEJOHN POLYNOMIALS 287
3 THE SECOND LITTLEJOHN POLYNOMIALS 289
4 KOEKOEK S GENERALIZED JACOBI TYPE POLYNOMIALS 290
XVII ORTHOGONAL POLYNOMIALS SATISFYING HIGHER ORDER DIFFERENTIAL
EQUATIONS
1 THE GENERALIZED JACOBI-TYPE POLYNOMIALS 291
2 THE GENERALIZED LAGUERRE-TYPE POLYNOMIALS {L M (IR)}~ =0 295
2F 1 / R~L
3 THE GENERALIZED LAGUERRE- TYPE POLYNOMIALS {LT 1 0)} = O 296
XVIII DIFFERENTIAL OPERATORS IN SOBOLEV SPACES
1 REGULAER SECOND ORDER SOBOLEV BOUNDARY VALUE PROBLEMS 302
2 REGULAER SOBOLEV BOUNDARY VALUE PROBLEMS FOR LINEAR HAMILTONIAN SYSTEMS
307
3 SINGULAR SECOND ORDER SOBOLEV BOUNDARY VALUE PROBLEMS 312
XIX EXAMPLES OF SOBOLEV DIFFERENTIAL OPERATORS
1 REGULAER SECOND ORDER OPERATORS 327
2 REGULAER HAMILTONIAN SYSTEMS 328
3 SINGULAR SECOND ORDER SOBOLEV BOUNDARY VALUE PROBLEMS 330
3.1 THE LAPLACIAN OPERATORS 330
3.2 THE BESSEL OPERATORS 331
3.3 THE JACOBI OPERATOR 333
3.4 THE GENERALIZED LAGUERRE OPERATOR 334
3.5 THE HERMITE OPERATOR 336
3.6 THE GENERALIZED EVEN HERMITE OPERATOR 336
3.7 THE GENERALIZED ODD HERMITE OPERATOR 336
IMAGE 7
XII CONTENTS
XX THE LEGENDRE-TYPE POLYNOMIALS AND THE LAGUERRE-TYPE POLYNOMIALS IN A
SOBOLEV SPACE
1 THE LEGENDRE-TYPE POLYNOMIALS 339
2 THE LAGUERRE-TYPE POLYNOMIALS 340
3 REMARKS 341
CLOSING REMARKS 343
INDEX 345
|
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| id | DE-604.BV014188048 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:59:14Z |
| institution | BVB |
| isbn | 3764367016 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009725434 |
| oclc_num | 248353908 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-824 DE-634 DE-83 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-824 DE-634 DE-83 DE-11 |
| physical | XIV, 352 S.: 24 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Krall, Allan M. Verfasser aut Hilbert Space, boundary value problems and orthogonal polynomials Allan M. Krall Problems and orthogonal polynomials Basel [u.a.] Birkhäuser 2002 XIV, 352 S.: 24 cm txt rdacontent n rdamedia nc rdacarrier Operator theory 133 Hamiltonsches System - Randwertproblem Hilbert-Raum - Linearer Operator Orthogonale Polynome Boundary value problems Hilbert space Orthogonal polynomials Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 s Linearer Operator (DE-588)4167721-3 s DE-604 Hamiltonsches System (DE-588)4139943-2 s Randwertproblem (DE-588)4048395-2 s Orthogonale Polynome (DE-588)4172863-4 s Operator theory 133 (DE-604)BV000000970 133 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009725434&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krall, Allan M. Hilbert Space, boundary value problems and orthogonal polynomials Operator theory Hamiltonsches System - Randwertproblem Hilbert-Raum - Linearer Operator Orthogonale Polynome Boundary value problems Hilbert space Orthogonal polynomials Hamiltonsches System (DE-588)4139943-2 gnd Hilbert-Raum (DE-588)4159850-7 gnd Linearer Operator (DE-588)4167721-3 gnd Randwertproblem (DE-588)4048395-2 gnd Orthogonale Polynome (DE-588)4172863-4 gnd |
| subject_GND | (DE-588)4139943-2 (DE-588)4159850-7 (DE-588)4167721-3 (DE-588)4048395-2 (DE-588)4172863-4 |
| title | Hilbert Space, boundary value problems and orthogonal polynomials |
| title_alt | Problems and orthogonal polynomials |
| title_auth | Hilbert Space, boundary value problems and orthogonal polynomials |
| title_exact_search | Hilbert Space, boundary value problems and orthogonal polynomials |
| title_full | Hilbert Space, boundary value problems and orthogonal polynomials Allan M. Krall |
| title_fullStr | Hilbert Space, boundary value problems and orthogonal polynomials Allan M. Krall |
| title_full_unstemmed | Hilbert Space, boundary value problems and orthogonal polynomials Allan M. Krall |
| title_short | Hilbert Space, boundary value problems and orthogonal polynomials |
| title_sort | hilbert space boundary value problems and orthogonal polynomials |
| topic | Hamiltonsches System - Randwertproblem Hilbert-Raum - Linearer Operator Orthogonale Polynome Boundary value problems Hilbert space Orthogonal polynomials Hamiltonsches System (DE-588)4139943-2 gnd Hilbert-Raum (DE-588)4159850-7 gnd Linearer Operator (DE-588)4167721-3 gnd Randwertproblem (DE-588)4048395-2 gnd Orthogonale Polynome (DE-588)4172863-4 gnd |
| topic_facet | Hamiltonsches System - Randwertproblem Hilbert-Raum - Linearer Operator Orthogonale Polynome Boundary value problems Hilbert space Orthogonal polynomials Hamiltonsches System Hilbert-Raum Linearer Operator Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009725434&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT krallallanm hilbertspaceboundaryvalueproblemsandorthogonalpolynomials AT krallallanm problemsandorthogonalpolynomials |