An introduction to operator polynomials:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1989
|
| Series: | Operator theory
38 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 389 S. |
| ISBN: | 3764323248 0817623248 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV001788267 | ||
| 003 | DE-604 | ||
| 005 | 20190502 | ||
| 007 | t | ||
| 008 | 890816s1989 |||| 00||| eng d | ||
| 020 | |a 3764323248 |9 3-7643-2324-8 | ||
| 020 | |a 0817623248 |9 0-8176-2324-8 | ||
| 035 | |a (OCoLC)19589025 | ||
| 035 | |a (DE-599)BVBBV001788267 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-19 |a DE-12 |a DE-91G |a DE-739 |a DE-355 |a DE-824 |a DE-706 |a DE-634 |a DE-188 |a DE-11 | ||
| 050 | 0 | |a QA404.5 | |
| 082 | 0 | |a 515/.55 |2 20 | |
| 084 | |a SK 620 |0 (DE-625)143249: |2 rvk | ||
| 100 | 1 | |a Rodman, Leiba |d 1949-2015 |e Verfasser |0 (DE-588)130488631 |4 aut | |
| 245 | 1 | 0 | |a An introduction to operator polynomials |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1989 | |
| 300 | |a XII, 389 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator theory |v 38 | |
| 650 | 7 | |a Opérateurs, Théorie des |2 ram | |
| 650 | 7 | |a Polynômes orthogonaux |2 ram | |
| 650 | 4 | |a espace Banach | |
| 650 | 4 | |a factorisation Wiener-Hopf | |
| 650 | 4 | |a opérateur Bézout | |
| 650 | 4 | |a opérateur Vandermonde | |
| 650 | 4 | |a polynôme opérateur | |
| 650 | 4 | |a théorie opérateur | |
| 650 | 4 | |a Operator theory | |
| 650 | 4 | |a Orthogonal polynomials | |
| 650 | 0 | 7 | |a Polynom |0 (DE-588)4046711-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Operatorpolynom |0 (DE-588)4246783-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Banach-Raum |0 (DE-588)4004402-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Linearer Operator |0 (DE-588)4167721-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Linearer Operator |0 (DE-588)4167721-3 |D s |
| 689 | 0 | 1 | |a Banach-Raum |0 (DE-588)4004402-6 |D s |
| 689 | 0 | 2 | |a Polynom |0 (DE-588)4046711-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Operatorpolynom |0 (DE-588)4246783-4 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Operator theory |v 38 |w (DE-604)BV000000970 |9 38 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001205125&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001205125 | ||
Record in the Search Index
| _version_ | 1804116281685704704 |
|---|---|
| adam_text | ix
TABLE OF CONTENTS
INTRODUCTION 1
CHAPTER 1. LINEARIZATIONS 8
1.1 Definitions and examples 8
1.2 Uniqueness of linearization 14
1.3 Existence of linearizations 19
1.4 Operator polynomials that are multiples
of Identity modulo compacts 22
1.5 Inverse linearization of operator polynomials . . 27
1.6 Exercises 35
1.7 Notes 37
CHAPTER 2. REPRESENTATIONS AND DIVISORS
OF MONIC OPERATOR POLYNOMIALS 39
2.1 Spectral pairs 39
2.2 Representations in terms of spectral pairs ... 44
2.3 Linearizations 47
2.4 Generalizations of canonical forms 50
2.5 Spectral triples 52
2.6 Multiplication and division theorems 56
2.7 Characterization of divisors in terms
of subspaces 61
2.8 Factorable indexless polynomials 66
2.9 Description of the left quotients 75
2.10 Spectral divisors 82
2.11 Differential and difference equations 83
2.12 Exercises 88
2.13 Notes 91
CHAPTER 3. VANDERMONDE OPERATORS AND COMMON MULTIPLES . . 93
3.1 Definition and basic properties
of the Vandermonde operator 93
X
3.2 Existence of common multiples 98
3.3 Common multiples of minimal degree 104
3.4 Fredholm Vandermonde operators 107
3.5 Vandermonde operators of divisors 109
3.6 Divisors with disjoint spectra 114
Appendix: Hulls of operators 116
3.7 Application to differential equations 120
3.8 Interpolation problem 122
3.9 Exercises 124
3.10 Notes 128
CHAPTER 4. STABLE FACTORIZATIONS OF MONIC
OPERATOR POLYNOMIALS 130
4.1 The metric space of subspaces in
a Banach space 130
4.2 Spherical gap and direct sums 137
4.3 Stable invariant subspaces 143
4.4 Proof of Theorems 4.3.3 and 4.3.4 147
4.5 Lipschitz stable invariant subspaces
and one sided resolvents . . 153
4.6 Lipschitz continuous dependence of
supporting subspaces and factorizations 160
4.7 Stability of factorizations of monic
operator polynomials 166
4.8 Stable sets of invariant subspaces 172
4.9 Exercises 175
4.10 Notes 176
CHAPTER 5. SELF ADJOINT OPERATOR POLYNOMIALS 178
5.1 Indefinite scalar products and subspaces .... 179
5.2 J self adjoint and J positizable operators . . . 183
xi
5.3 Factorizations and invariant
semidefinite subspaces 185
5.4 Classes of polynomials with special
factorizations 195
5.5 Positive semidefinite operator polynomials . . . 197
5.6 Strongly hyperbolic operator polynomials .... 199
5.7 Proof of Theorem 5.6.4 202
5.8 Invariant subspaces for unitary and
self adjoint operators in indefinite
scalar products ; 208
5.9 Self adjoint operator polynomials
of second degree 216
5.10 Exercises 220
5.11 Notes 222
CHAPTER 6. SPECTRAL TRIPLES AND DIVISIBILITY OF
NON MONIC OPERATOR POLYNOMIALS 224
6.1 Spectral triples: definition and uniqueness . . . 224
6.2 Calculus of spectral triples 231
6.3 Construction of spectral triples 241
6.4 Spectral triples and linearization 251
6.5 Spectral triples and divisibility 254
6.6 Characterization of spectral pairs 260
6.7 Reduction to raonic polynomials 263
6.8 Exercises 268
6.9 Notes 268
CHAPTER 7. POLYNOMIALS WITH GIVEN SPECTRAL PAIRS
AND EXACTLY CONTROLLABLE SYSTEMS 269
7.1 Exactly controllable systems 269
7.2 Spectrum assignment theorems 273
7.3 Analytic dependence of the feedback 284
7.4 Polynomials with given spectral pairs 287
xii
7.5 Invariant subspaces and divisors 292
7.6 Exercises 294
7.7 Notes 296
CHAPTER 8. COMMON DIVISORS AND COMMON MULTIPLES 297
8.1 Common divisors 297
8.2 Common multiples 300
8.3 Coprimeness and Bezout equation 306
8.4 Analytic behavior of common multiples 311
8.5 Notes 316
CHAPTER 9. RESULTANT AND BEZOUTIAN OPERATORS 317
9.1 Resultant operators and their kernel 317
9.2 Proof of Theorem 9.1.4 322
9.3 Bezoutian operator 329
9.4 The kernel of a Bezoutian operator 333
9.5 Inertia theorems 338
9.6 Spectrum separation 344
9.7 Spectrum separation problem: deductions
and special cases 355
9.8 Applications to difference equations 358
9.9 Notes 359
CHAPTER 10. WIENER HOPF FACTORIZATION 361
10.1 Definition and the main result 361
10.2 Pairs of finite type and proof
of Theorem 10.1.1 364
10.3 Finite dimensional perturbations 366
10.4 Notes 370
REFERENCES 371
Notation 385
Index 387
|
| any_adam_object | 1 |
| author | Rodman, Leiba 1949-2015 |
| author_GND | (DE-588)130488631 |
| author_facet | Rodman, Leiba 1949-2015 |
| author_role | aut |
| author_sort | Rodman, Leiba 1949-2015 |
| author_variant | l r lr |
| building | Verbundindex |
| bvnumber | BV001788267 |
| callnumber-first | Q - Science |
| callnumber-label | QA404 |
| callnumber-raw | QA404.5 |
| callnumber-search | QA404.5 |
| callnumber-sort | QA 3404.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 620 |
| ctrlnum | (OCoLC)19589025 (DE-599)BVBBV001788267 |
| dewey-full | 515/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.55 |
| dewey-search | 515/.55 |
| dewey-sort | 3515 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02150nam a2200577 cb4500</leader><controlfield tag="001">BV001788267</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20190502 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">890816s1989 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3764323248</subfield><subfield code="9">3-7643-2324-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0817623248</subfield><subfield code="9">0-8176-2324-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)19589025</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV001788267</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA404.5</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.55</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 620</subfield><subfield code="0">(DE-625)143249:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rodman, Leiba</subfield><subfield code="d">1949-2015</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)130488631</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">An introduction to operator polynomials</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Basel [u.a.]</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">1989</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XII, 389 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Operator theory</subfield><subfield code="v">38</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Opérateurs, Théorie des</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Polynômes orthogonaux</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">espace Banach</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">factorisation Wiener-Hopf</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">opérateur Bézout</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">opérateur Vandermonde</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">polynôme opérateur</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">théorie opérateur</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operator theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Orthogonal polynomials</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Polynom</subfield><subfield code="0">(DE-588)4046711-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Operatorpolynom</subfield><subfield code="0">(DE-588)4246783-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Banach-Raum</subfield><subfield code="0">(DE-588)4004402-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Linearer Operator</subfield><subfield code="0">(DE-588)4167721-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Linearer Operator</subfield><subfield code="0">(DE-588)4167721-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Banach-Raum</subfield><subfield code="0">(DE-588)4004402-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Polynom</subfield><subfield code="0">(DE-588)4046711-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Operatorpolynom</subfield><subfield code="0">(DE-588)4246783-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Operator theory</subfield><subfield code="v">38</subfield><subfield code="w">(DE-604)BV000000970</subfield><subfield code="9">38</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001205125&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001205125</subfield></datafield></record></collection> |
| id | DE-604.BV001788267 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:36:01Z |
| institution | BVB |
| isbn | 3764323248 0817623248 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001205125 |
| oclc_num | 19589025 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-12 DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-824 DE-706 DE-634 DE-188 DE-11 |
| owner_facet | DE-19 DE-BY-UBM DE-12 DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-824 DE-706 DE-634 DE-188 DE-11 |
| physical | XII, 389 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Rodman, Leiba 1949-2015 Verfasser (DE-588)130488631 aut An introduction to operator polynomials Basel [u.a.] Birkhäuser 1989 XII, 389 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 38 Opérateurs, Théorie des ram Polynômes orthogonaux ram espace Banach factorisation Wiener-Hopf opérateur Bézout opérateur Vandermonde polynôme opérateur théorie opérateur Operator theory Orthogonal polynomials Polynom (DE-588)4046711-9 gnd rswk-swf Operatorpolynom (DE-588)4246783-4 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Linearer Operator (DE-588)4167721-3 s Banach-Raum (DE-588)4004402-6 s Polynom (DE-588)4046711-9 s DE-604 Operatorpolynom (DE-588)4246783-4 s Operator theory 38 (DE-604)BV000000970 38 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001205125&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rodman, Leiba 1949-2015 An introduction to operator polynomials Operator theory Opérateurs, Théorie des ram Polynômes orthogonaux ram espace Banach factorisation Wiener-Hopf opérateur Bézout opérateur Vandermonde polynôme opérateur théorie opérateur Operator theory Orthogonal polynomials Polynom (DE-588)4046711-9 gnd Operatorpolynom (DE-588)4246783-4 gnd Banach-Raum (DE-588)4004402-6 gnd Linearer Operator (DE-588)4167721-3 gnd |
| subject_GND | (DE-588)4046711-9 (DE-588)4246783-4 (DE-588)4004402-6 (DE-588)4167721-3 |
| title | An introduction to operator polynomials |
| title_auth | An introduction to operator polynomials |
| title_exact_search | An introduction to operator polynomials |
| title_full | An introduction to operator polynomials |
| title_fullStr | An introduction to operator polynomials |
| title_full_unstemmed | An introduction to operator polynomials |
| title_short | An introduction to operator polynomials |
| title_sort | an introduction to operator polynomials |
| topic | Opérateurs, Théorie des ram Polynômes orthogonaux ram espace Banach factorisation Wiener-Hopf opérateur Bézout opérateur Vandermonde polynôme opérateur théorie opérateur Operator theory Orthogonal polynomials Polynom (DE-588)4046711-9 gnd Operatorpolynom (DE-588)4246783-4 gnd Banach-Raum (DE-588)4004402-6 gnd Linearer Operator (DE-588)4167721-3 gnd |
| topic_facet | Opérateurs, Théorie des Polynômes orthogonaux espace Banach factorisation Wiener-Hopf opérateur Bézout opérateur Vandermonde polynôme opérateur théorie opérateur Operator theory Orthogonal polynomials Polynom Operatorpolynom Banach-Raum Linearer Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001205125&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT rodmanleiba anintroductiontooperatorpolynomials |