Operator theory for electromagnetics: an introduction
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2002
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XIX, 634 S. Ill., graph. Darst. |
| ISBN: | 0387952780 |
Internformat
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| 245 | 1 | 0 | |a Operator theory for electromagnetics |b an introduction |c George W. Hanson ; Alexander B. Yakovlev |
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Datensatz im Suchindex
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|---|---|
| adam_text | GEORGE W. HANSON ALEXANDER B. YAKOVLEV OPERATOR THEORY FOR
ELECTROMAGNETIC S AN INTRODUCTION WITH 77 ILLUSTRATIONS SPRINGER
CONTENTS PREFACE VII LIST OF SYMBOLS AND NOTATION XVII PART I: BASIC
THEORY 1 1 ELECTROMAGNETIC FUNDAMENTALS 3 1.1 MAXWELL S EQUATIONS 4
1.1.1 MAXWELL S EQUATIONS*DIFFERENTIAL FORM 4 1.1.2 MAXWELL S
EQUATIONS*INTEGRAL FORM 6 1.1.3 BOUNDARY CONDITIONS 7 1.1.4
TIME-HARMONIC AND TRANSFORM-DOMAIN FIELDS ... 7 1.2 FIELD THEOREMS 13
1.2.1 DUALITY : . . . 13 1.2.2 POYNTING S THEOREM 14 1.2.3 THE LORENTZ
RECIPROCITY THEOREM 15 1.3 WAVE EQUATIONS 17 1.3.1 VECTOR WAVE AND
VECTOR HELMHOLTZ EQUATIONS FOR ELECTRIC AND MAGNETIC FIELDS 17 1.3.2
VECTOR AND SCALAR POTENTIALS AND ASSOCIATED HELMHOLTZ EQUATIONS 18 1.3.3
SOLUTION OF THE SCALAR HELMHOLTZ EQUATIONS AND SCALAR GREEN S FUNCTIONS
20 1.3.4 IMPROPER INTEGRALS ASSOCIATED WITH SCALAR GREEN S FUNCTIONS
.... * 26 1.3.5 SOLUTION OF THE VECTOR WAVE AND VECTOR HELMHOLTZ
EQUATIONS*DYADIC GREEN S FUNCTIONS AND ASSOCIATED IMPROPER INTEGRALS 38
1.4 INTEGRAL EQUATIONS 48 1.4.1 DOMAIN INTEGRAL EQUATIONS 48 1.4.2
SURFACE INTEGRAL EQUATIONS 52 1.5 UNIQUENESS THEOREM AND RADIATION
CONDITIONS . 55 BIBLIOGRAPHY 59 IX CONTENTS INTRODUCTORY FUNCTIONAL
ANALYSIS 63 2.1 SETS 64 2.1.1 SETS OF NUMBERS 64 2.1.2 SETS OF
FUNCTIONS*FUNCTION SPACES 65 2.1.3 SETS OF SEQUENCES*SEQUENCE SPACES 73
2.2 METRIC SPACE 83 2.2.1 CONTINUITY AND CONVERGENCE 88 2.2.2 DENSENESS,
CLOSURE, AND COMPACTNESS 94 2.2.3 COMPLETENESS 97 2.3 LINEAR SPACE 100
2.3.1 LINEAR SUBSPACE 101 2.3.2 DIMENSION OF A LINEAR SPACE, BASIS 103
2.4 NORMED LINEAR SPACE 105 2.4.1 COMPLETENESS, BANACH SPACE 109 2.5
INNER PRODUCT SPACE 110 2.5.1 INNER PRODUCT 110 2.5.2 PSEUDO INNER
PRODUCT, REACTION 113 2.5.3 STRONG AND WEAK CONVERGENCE 114 2.5.4
COMPLETENESS, HILBERT SPACE 115 2.5.5 ORTHOGONALITY 116 2.5.6 EXPANSIONS
AND PROJECTIONS 117 2.5.7 BASIS OF A HILBERT SPACE 121 BIBLIOGRAPHY 125
INTRODUCTORY LINEAR OPERATOR THEORY 129 3.1 LINEAR OPERATORS 130 3.1.1
GENERAL CONCEPTS 130 3.1.2 EXAMPLES RELATED TO LINEAR OPERATORS 134
3.1.3 ISOMORPHISMS 141 3.2 LINEAR FUNCTIONALS I 143 3.2.1 GENERAL
CONCEPTS . . . [ 143 3.2.2 EXAMPLES RELATED TO LINEAR FUNCTIONALS 144
3.3 ADJOINT OPERATORS 146 3.3.1 GENERAL CONCEPTS: BOUNDED OPERATORS 146
3.3.2 EXAMPLES OF OPERATOR ADJOINTS: BOUNDED OPERATORS 147 3.3.3 GENERAL
CONCEPTS: UNBOUNDED OPERATORS 149 3.3.4 EXAMPLES OF OPERATOR ADJOINTS:
UNBOUNDED OPERATORS 150 3.4 SELF-ADJOINT, SYMMETRIC, NORMAL, AND UNITARY
OPERATORS . 154 3.4.1 GENERAL CONCEPTS 154 3.4.2 EXAMPLES RELATING TO
SELF-ADJOINTNESS 158 3.4.3 PSEUDO ADJOINTS, PSEUDO SYMMETRY, AND
RECIPROCITY 161 3.5 DEFINITENESS AND CONVERGENCE IN ENERGY 164 CONTENTS
XI 3.5.1 GENERAL CONCEPTS 164 3.5.2 EXAMPLES RELATING TO DEFINITENESS
166 3.5.3 CONVERGENCE IN ENERGY 167 3.6 COMPACT OPERATORS 169 3.6.1
GENERAL CONCEPTS 169 3.6.2 EXAMPLES RELATING TO COMPACTNESS 171 3.7
CONTINUITY AND COMPACTNESS OF MATRIX OPERATORS 175 3.7.1 MATRIX
OPERATORS IN I 2 176 3.7.2 GRIBANOV S THEOREMS 177 3.8 CLOSED AND
CLOSABLE OPERATORS 180 3.9 INVERTIBLE OPERATORS 181 3.9.1 GENERAL
CONCEPTS 181 3.9.2 EXAMPLES RELATING TO INVERSES 189 3.9.3 GREEN S
FUNCTIONS AND GREEN S OPERATORS 190 3.10 PROJECTION OPERATORS 202 3.11
SOLUTION OF OPERATOR EQUATIONS 204 3.11.1 EXISTENCE OF SOLUTIONS 204
3.11.2 CONVERGENCE OF SOLUTIONS 207 BIBLIOGRAPHY 213 4 SPECTRAL THEORY
OF LINEAR OPERATORS 219 4.1 GENERAL CONCEPTS 220 4.1.1 OPERATORS ON
FINITE-DIMENSIONAL SPACES 222 4.1.2 OPERATORS ON INFINITE-DIMENSIONAL
SPACES 223 4.2 SPECTRAL PROPERTIES OF OPERATORS 228 4.2.1 GENERAL
PROPERTIES 228 4.2.2 BOUNDED OPERATORS 232 4.2.3 INVERTIBLE OPERATORS
233 4.2.4 COMPACT OPERATORS 234 4.2.5 SELF-ADJOINT OPERATORS .. 234
4.2.6 NONNEGATIVE AND POSITIVE OPERATORS 236 4.2.7 COMPACT SELF-ADJOINT
OPERATORS 236 4.2.8 NORMAL AND UNITARY OPERATORS 237 4.2.9 GENERALIZED
EIGENVALUE PROBLEMS 239 4.2.10 EIGENVALUE PROBLEMS UNDER A PSEUDO INNER
PRODUCT 241 4.2.11 PSEUDO SELF-ADJOINT, NONSTANDARD EIGENVALUE PROBLEMS
242 4.2.12 STEINBERG S THEOREMS FOR COMPACT OPERATORS . . . . 244 4.3
EXPANSIONS AND REPRESENTATIONS, SPECTRAL THEOREMS . . . . 247 4.3.1
OPERATORS ON FINITE-DIMENSIONAL SPACES 248 4.3.2 OPERATORS ON
INFINITE-DIMENSIONAL SPACES 257 4.3.3 SPECTRAL EXPANSIONS ASSOCIATED
WITH BOUNDARY VALUE PROBLEMS 260 XII CONTENTS 4.3.4 SPECTRAL EXPANSIONS
ASSOCIATED WITH INTEGRAL OPERATORS 263 4.3.5 GENERALIZED EIGENVECTORS
AND THE ROOT SYSTEM . . . 269 4.3.6 SPECTRAL REPRESENTATIONS 271 4.4
FUNCTIONS OF OPERATORS 273 4.4.1 FUNCTIONS OF OPERATORS VIA SPECTRAL
REPRESENTATIONS 273 4-4.2 FUNCTIONS OF OPERATORS VIA SERIES EXPANSIONS
.... 276 4.4.3 FUNCTIONS OF OPERATORS VIA THE DUNFORD INTEGRAL
REPRESENTATION 277 4.5 SPECTRAL METHODS IN THE SOLUTION OF OPERATOR
EQUATIONS . . 278 4.5.1 FIRST- AND SECOND-KIND OPERATOR EQUATIONS 279
4.5.2 SPECTRAL METHODS AND GREEN S FUNCTIONS 282 4.5.3 CONVERGENCE OF
NONSTANDARD EIGENVALUES IN PROJECTION TECHNIQUES . 285 BIBLIOGRAPHY 287
5 STURM*LIOUVILLE OPERATORS 291 5.1 REGULAR STURM-LIOUVILLE PROBLEMS 292
5.1.1 SPECTRAL PROPERTIES OF THE REGULAR STURM-LIOUVILLE OPERATOR 294
5.1.2 SOLUTION OF THE REGULAR STURM-LIOUVILLE PROBLEM 297 5.1.3
EIGENFUNCTION EXPANSION SOLUTION OF THE REGULAR STURM-LIOUVILLE PROBLEM
303 5.1.4 COMPLETENESS RELATIONS FOR THE REGULAR STURM-LIOUVILLE PROBLEM
305 5.2 SINGULAR STURM-LIOUVILLE PROBLEMS 307 5.2.1 CLASSIFICATION OF
SINGULAR POINTS 311 5.2.2 IDENTIFICATION OF THE CONTINUOUS SPECTRUM AND
IMPROPER EIGENFUNCTIONS 314 5.2.3 CONTINUOUS EXPANSIONS AND ASSOCIATED
INTEGRAL TRANSFORMS 321 5.2.4 SIMULTANEOUS OCCURRENCE OF DISCRETE AND
CONTINUOUS SPECTRA 326 5.3 NONSELF-ADJOINT STURM-LIOUVILLE PROBLEMS 327
5.3.1 GREEN S FUNCTION METHODS IN THE NONSELF- ADJOINT CASE 327 5.3.2
SPECTRAL METHODS IN THE NONSELF-ADJOINT CASE . . . . 331 5.4 SPECIAL
FUNCTIONS ASSOCIATED WITH SINGULAR STURM-LIOUVILLE PROBLEMS 340 5.4.1
CYLINDRICAL COORDINATE PROBLEMS 341 5.4.2 SPHERICAL COORDINATE PROBLEMS
350 5.5 CLASSICAL ORTHOGONAL POLYNOMIALS AND ASSOCIATED BASES 358
CONTENTS XIII 5.5.1 LAGUERRE POLYNOMIALS 359 5.5.2 HERMITE POLYNOMIALS
359 5.5.3 CHEBYSHEV POLYNOMIALS 360 BIBLIOGRAPHY 363 PART II:
APPLICATIONS IN ELECTROMAGNETICS 365 6 POISSON S AND LAPLACE S BOUNDARY
VALUE PROBLEMS: POTENTIAL THEORY 367 6.1 PROBLEM FORMULATION 368 6.2
OPERATOR PROPERTIES OF THE NEGATIVE LAPLACIAN 372 6.3 SPECTRAL
PROPERTIES OF THE NEGATIVE LAPLACIAN 376 6.4 SOLUTION TECHNIQUES FOR
SELF-ADJOINT PROBLEMS 378 6.5 INTEGRAL METHODS AND SEPARATION OF
VARIABLES SOLUTIONS FOR NONSELF-ADJOINT PROBLEMS 384 6.6 INTEGRAL
EQUATION TECHNIQUES FOR POTENTIAL THEORY 391 7 TRANSMISSION-LINE
ANALYSIS 403 7.1 GENERAL ANALYSIS 404 7.2 TRANSMISSION-LINE RESONATORS
412 7.3 SEMI-INFINITE AND INFINITE TRANSMISSION LINES 415 7.4
MULTICONDUCTOR TRANSMISSION LINES 417 8 PLANARLY LAYERED MEDIA PROBLEMS
421 8.1 TWO-DIMENSIONAL PROBLEMS 422 8.1.1 GENERAL ANALYSIS 422 8.1.2
HOMOGENEOUSLY FILLED PARALLEL-PLATES 434 8.1.3 TWO-DIMENSIONAL RESONATOR
444 8.1.4 SEMI-OPEN STRUCTURE ., 446 8.1.5 FREE SPACE 446 8.1.6
IMPEDANCE PLANE STRUCTURE 447 8.1.7 GROUNDED DIELECTRIC LAYER 462 8.1.8
COMMENTS ON GENERAL MULTILAYERED MEDIA PROBLEMS, COMPLETENESS, AND
ASSOCIATED EIGENFUNCTIONS 480 8.2 TWO-DIMENSIONAL SCATTERING PROBLEMS IN
PLANAR MEDIA . . 482 8.2.1 TE SCATTERING FROM INHOMOGENEOUS DIELECTRIC
CYLINDERS IN LAYERED MEDIA 482 8.2.2 TE SCATTERING FROM THIN CONDUCTING
STRIPS IN LAYERED MEDIA 486 8.3 THREE-DIMENSIONAL PLANAR PROBLEMS 489
8.3.1 GENERAL ANALYSIS . . : 490 8.3.2 PARALLEL-PLATE STRUCTURE 499 XIV
CONTENTS 9 CYLINDRICAL WAVEGUIDE PROBLEMS 503 9.1 SCATTERING PROBLEMS
FOR WAVEGUIDES FILLED WITH A HOMOGENEOUS MEDIUM 504 9.1.1 GREEN S
DYADICS*GENERAL CONCEPTS AND DEFINITIONS 504 9.1.2 INFINITE WAVEGUIDE
CONTAINING METAL OBSTACLES . . . 507 9.1.3 INFINITE WAVEGUIDE WITH
APERTURES 512 9.1.4 SEMI-INFINITE WAVEGUIDES COUPLED THROUGH APERTURES
IN A COMMON GROUND PLANE 515 9.1.5 SEMI-INFINITE WAVEGUIDES WITH METAL
OBSTACLES COUPLED THROUGH APERTURES IN A COMMON GROUND PLANE 516 9.2
GREEN S DYADICS FOR WAVEGUIDES FILLED WITH A HOMOGENEOUS MEDIUM 518
9.2.1 MAGNETIC POTENTIAL GREEN S DYADICS 519 9.2.2 ELECTRIC GREEN S
DYADICS 526 9.3 SCATTERING PROBLEMS FOR WAVEGUIDES FILLED WITH A
PLANARLY LAYERED MEDIUM 532 9.3.1 INTERACTING ELECTRIC- AND
MAGNETIC-TYPE DISCONTINUITIES IN A LAYERED-MEDIUM WAVEGUIDE . . 532
9.3.2 A WAVEGUIDE-BASED APERTURE-COUPLED PATCH ARRAY 546 9.4 ELECTRIC
GREEN S DYADICS FOR WAVEGUIDES FILLED WITH A PLANARLY LAYERED MEDIUM 553
9.4.1 ELECTRIC GREEN S DYADICS OF THE THIRD KIND 554 9.5 THE METHOD OF
OVERLAPPING REGIONS 560 9.5.1 INTEGRAL EQUATION FORMULATIONS FOR
OVERLAPPING REGIONS 561 9.5.2 SHIELDED MICROSTRIP LINE 567 10
ELECTROMAGNETIC CAVITIES 575 10.1 PROBLEM FORMULATION 575 10.2 OPERATOR
PROPERTIES AND EIGENFUNCTION METHODS 577 10.3 INTEGRAL EQUATION METHODS
FOR CAVITIES 586 10.4 CAVITY RESONANCES FROM VECTOR POTENTIALS 589
BIBLIOGRAPHY FOR PART II 597 A VECTOR, DYADIC, AND INTEGRAL RELATIONS
605 A.I VECTOR IDENTITIES 605 A.2 DYADIC IDENTITIES 606 A.3 DYADIC
ANALYSIS 607 A.4 INTEGRAL IDENTITIES 608 A.5 USEFUL FORMULAS INVOLVING
THE POSITION VECTOR AND SCALAR GREEN S FUNCTIONS 611 CONTENTS XV A.6
SCALAR AND VECTOR DIFFERENTIAL OPERATORS IN THE THREE PRINCIPAL
COORDINATE SYSTEMS 612 B DERIVATION OF SECOND-DERIVATIVE FORMULA (1.59)
615 C GRAM-SCHMIDT ORTHOGONALIZATION PROCEDURE 619 D COEFFICIENTS OF
PLANAR-MEDIA GREEN S DYADICS 621 E ADDITIONAL FUNCTION SPACES 625 INDEX
629
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| any_adam_object | 1 |
| author | Hanson, George W. 1963- Yakovlev, Alexander B. |
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| author_facet | Hanson, George W. 1963- Yakovlev, Alexander B. |
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| ctrlnum | (OCoLC)46240276 (DE-599)BVBBV014087487 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.14/1 |
| dewey-search | 530.14/1 |
| dewey-sort | 3530.14 11 |
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| discipline | Physik Elektrotechnik Elektrotechnik / Elektronik / Nachrichtentechnik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:57:25Z |
| institution | BVB |
| isbn | 0387952780 |
| language | English |
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| publisher | Springer |
| record_format | marc |
| spelling | Hanson, George W. 1963- Verfasser (DE-588)173507018 aut Operator theory for electromagnetics an introduction George W. Hanson ; Alexander B. Yakovlev New York [u.a.] Springer 2002 XIX, 634 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturangaben Electromagnetic theory Operator theory Elektrodynamik (DE-588)4014251-6 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Elektrodynamik (DE-588)4014251-6 s Funktionalanalysis (DE-588)4018916-8 s Operatortheorie (DE-588)4075665-8 s DE-604 Yakovlev, Alexander B. Verfasser aut Erscheint auch als Online-Ausgabe 978-1-4419-2934-1 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009650007&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hanson, George W. 1963- Yakovlev, Alexander B. Operator theory for electromagnetics an introduction Electromagnetic theory Operator theory Elektrodynamik (DE-588)4014251-6 gnd Funktionalanalysis (DE-588)4018916-8 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4014251-6 (DE-588)4018916-8 (DE-588)4075665-8 |
| title | Operator theory for electromagnetics an introduction |
| title_auth | Operator theory for electromagnetics an introduction |
| title_exact_search | Operator theory for electromagnetics an introduction |
| title_full | Operator theory for electromagnetics an introduction George W. Hanson ; Alexander B. Yakovlev |
| title_fullStr | Operator theory for electromagnetics an introduction George W. Hanson ; Alexander B. Yakovlev |
| title_full_unstemmed | Operator theory for electromagnetics an introduction George W. Hanson ; Alexander B. Yakovlev |
| title_short | Operator theory for electromagnetics |
| title_sort | operator theory for electromagnetics an introduction |
| title_sub | an introduction |
| topic | Electromagnetic theory Operator theory Elektrodynamik (DE-588)4014251-6 gnd Funktionalanalysis (DE-588)4018916-8 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Electromagnetic theory Operator theory Elektrodynamik Funktionalanalysis Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009650007&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hansongeorgew operatortheoryforelectromagneticsanintroduction AT yakovlevalexanderb operatortheoryforelectromagneticsanintroduction |