Spectral theory of operator pencils, Hermite-Biehler functions, and their applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cham [u.a.]
Birkhäuser Springer
2015
|
| Schriftenreihe: | Operator Theory
246 |
| Schlagworte: | |
| Online-Zugang: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource (XVII, 412 S.) 11 illus |
| ISBN: | 9783319170701 |
| ISSN: | 0255-0156 |
| DOI: | 10.1007/978-3-319-17070-1 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804174858748166144 |
|---|---|
| adam_text | SPECTRAL THEORY OF OPERATOR PENCILS, HERMITE-BIEHLER FUNCTIONS, AND
THEIR APPLICATIONS
/ MOELLER, MANFRED
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PREFACE
PART I: OPERATOR PENCILS
1.QUADRATIC OPERATOR PENCILS
2.APPLICATIONS OF QUADRATIC OPERATOR PENCILS
3.OPERATOR PENCILS WITH ESSENTIAL SPECTRUM
4.OPERATOR PENCILS WITH A GYROSCOPIC TERM
PART II: HERMITE–BIEHLER FUNCTIONS
5.GENERALIZED HERMITE–BIEHLER FUNCTIONS
6.APPLICATIONS OF SHIFTED HERMITE–BIEHLER FUNCTIONS
PART III: DIRECT AND INVERSE PROBLEMS
7.EIGENVALUE ASYMPTOTICS
8.INVERSE PROBLEMS
PART IV: BACKGROUND MATERIAL
9.SPECTRAL DEPENDENCE ON A PARAMETER
10.SOBOLEV SPACES AND DIFFERENTIAL OPERATORS
11.ANALYTIC AND MEROMORPHIC FUNCTIONS
12.INVERSE STURM–LIOUVILLE PROBLEMS
BIBLIOGRAPHY
INDEX
INDEX OF NOTATION
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
SPECTRAL THEORY OF OPERATOR PENCILS, HERMITE-BIEHLER FUNCTIONS, AND
THEIR APPLICATIONS
/ MOELLER, MANFRED
: 2015
ABSTRACT / INHALTSTEXT
THE THEORETICAL PART OF THIS MONOGRAPH EXAMINES THE DISTRIBUTION OF THE
SPECTRUM OF OPERATOR POLYNOMIALS, FOCUSING ON QUADRATIC OPERATOR
POLYNOMIALS WITH DISCRETE SPECTRA. THE SECOND PART IS DEVOTED TO
APPLICATIONS. STANDARD SPECTRAL PROBLEMS IN HILBERT SPACES ARE OF THE
FORM A-ΛI FOR AN OPERATOR A, AND SELF-ADJOINT OPERATORS ARE OF
PARTICULAR INTEREST AND IMPORTANCE, BOTH THEORETICALLY AND IN TERMS OF
APPLICATIONS. A CHARACTERISTIC FEATURE OF SELF-ADJOINT OPERATORS IS THAT
THEIR SPECTRA ARE REAL, AND MANY SPECTRAL PROBLEMS IN THEORETICAL
PHYSICS AND ENGINEERING CAN BE DESCRIBED BY USING THEM. HOWEVER, A LARGE
CLASS OF PROBLEMS, IN PARTICULAR VIBRATION PROBLEMS WITH BOUNDARY
CONDITIONS DEPENDING ON THE SPECTRAL PARAMETER, ARE REPRESENTED BY
OPERATOR POLYNOMIALS THAT ARE QUADRATIC IN THE EIGENVALUE PARAMETER AND
WHOSE COEFFICIENTS ARE SELF-ADJOINT OPERATORS. THE SPECTRA OF SUCH
OPERATOR POLYNOMIALS ARE IN GENERAL NO MORE REAL, BUT STILL EXHIBIT
CERTAIN PATTERNS. THE DISTRIBUTION OF THESE SPECTRA IS THE MAIN FOCUS OF
THE PRESENT VOLUME. FOR SOME CLASSES OF QUADRATIC OPERATOR POLYNOMIALS,
INVERSE PROBLEMS ARE ALSO CONSIDERED. THE CONNECTION BETWEEN THE SPECTRA
OF SUCH QUADRATIC OPERATOR POLYNOMIALS AND GENERALIZED HERMITE-BIEHLER
FUNCTIONS IS DISCUSSED IN DETAIL. MANY APPLICATIONS ARE THOROUGHLY
INVESTIGATED, SUCH AS THE REGGE PROBLEM AND DAMPED VIBRATIONS OF SMOOTH
STRINGS, STIELTJES STRINGS, BEAMS, STAR GRAPHS OF STRINGS AND QUANTUM
GRAPHS. SOME CHAPTERS SUMMARIZE ADVANCED BACKGROUND MATERIAL, WHICH IS
SUPPLEMENTED WITH DETAILED PROOFS. WITH REGARD TO THE READER’S
BACKGROUND KNOWLEDGE, ONLY THE BASIC PROPERTIES OF OPERATORS IN HILBERT
SPACES AND WELL-KNOWN RESULTS FROM COMPLEX ANALYSIS ARE ASSUMED
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Möller, Manfred Pivovarchik, Vyacheslav |
| author_GND | (DE-588)1022394428 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-17070-1 |
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| spelling | Möller, Manfred Verfasser (DE-588)1022394428 aut Spectral theory of operator pencils, Hermite-Biehler functions, and their applications Manfred Möller ; Vyacheslav Pivovarchik Cham [u.a.] Birkhäuser Springer 2015 1 Online-Ressource (XVII, 412 S.) 11 illus txt rdacontent c rdamedia cr rdacarrier Operator Theory 246 0255-0156 Mathematics Operator theory Differential Equations Operator Theory Ordinary Differential Equations Mathematical Physics Mathematik Pivovarchik, Vyacheslav Verfasser aut Erscheint auch als Druckausgabe 978-3-319-17069-5 Operator Theory Advances and Applications 246 (DE-604)BV035421307 246 https://doi.org/10.1007/978-3-319-17070-1 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028101470&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028101470&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Möller, Manfred Pivovarchik, Vyacheslav Spectral theory of operator pencils, Hermite-Biehler functions, and their applications Mathematics Operator theory Differential Equations Operator Theory Ordinary Differential Equations Mathematical Physics Mathematik |
| title | Spectral theory of operator pencils, Hermite-Biehler functions, and their applications |
| title_auth | Spectral theory of operator pencils, Hermite-Biehler functions, and their applications |
| title_exact_search | Spectral theory of operator pencils, Hermite-Biehler functions, and their applications |
| title_full | Spectral theory of operator pencils, Hermite-Biehler functions, and their applications Manfred Möller ; Vyacheslav Pivovarchik |
| title_fullStr | Spectral theory of operator pencils, Hermite-Biehler functions, and their applications Manfred Möller ; Vyacheslav Pivovarchik |
| title_full_unstemmed | Spectral theory of operator pencils, Hermite-Biehler functions, and their applications Manfred Möller ; Vyacheslav Pivovarchik |
| title_short | Spectral theory of operator pencils, Hermite-Biehler functions, and their applications |
| title_sort | spectral theory of operator pencils hermite biehler functions and their applications |
| topic | Mathematics Operator theory Differential Equations Operator Theory Ordinary Differential Equations Mathematical Physics Mathematik |
| topic_facet | Mathematics Operator theory Differential Equations Operator Theory Ordinary Differential Equations Mathematical Physics Mathematik |
| url | https://doi.org/10.1007/978-3-319-17070-1 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028101470&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028101470&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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