Meromorphic functions and linear algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2003]
|
| Schriftenreihe: | Fields Institute Monographs / Fields Institute for Research in Mathematical Sciences
18 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Vorwort: "This monograph is based on lectures which were given in two phases. In the fall of 1995 I gave a series of lectures at the Helsinki University of Technology and in October 2001 at the Fields Institute in Toronto." |
| Beschreibung: | x, 136 Seiten |
| ISBN: | 0821832476 9780821832479 |
Internformat
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| 245 | 1 | 0 | |a Meromorphic functions and linear algebra |c Olavi Nevanlinna |
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| 264 | 4 | |c © 2003 | |
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| 490 | 1 | |a Fields Institute Monographs / Fields Institute for Research in Mathematical Sciences |v 18 | |
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| 650 | 4 | |a Algèbre linéaire | |
| 650 | 4 | |a Fonctions méromorphes | |
| 650 | 4 | |a Algebras, Linear | |
| 650 | 4 | |a Functions, Meromorphic | |
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Meromorphe Funktion |0 (DE-588)4136862-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Meromorphe Funktion |0 (DE-588)4136862-9 |D s |
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| 810 | 2 | |a Fields Institute for Research in Mathematical Sciences |t Fields Institute Monographs |v 18 |w (DE-604)BV009737926 |9 18 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010125062 | |
Datensatz im Suchindex
| _version_ | 1807864644362043392 |
|---|---|
| adam_text |
CONTENTS
PREFACE ix
PROLOGUE 1
Tapping away in an evening at Djursholm 1
What does an epsilon weigh? 1
Red wine at the Stock Exchange Club 2
Ice cream in Madison 2
Exact equality 3
The deficiency of values 5
Zurich 5
Beautiful to look at, but. 6
The unbearable ease of using norms 6
Centenary Colloquium in Joensuu 7
Two basic tasks, stability first 7
And then accelerating the iteration 9
Factoring the resolvent 10
In the Hermann Weyl lecture hall 11
A quiet life in Warsaw 12
Finally, in Kirkkonummi 12
FIRST CHAPTER 15
Resolvent 15
Cauchy integral 20
SECOND CHAPTER 23
Entire functions 23
Taylor coefficients 24
Meromorphic functions 25
The first main theorem 30
Cartan's identity 31
Order and type for meromorphic functions 32
Boutroux Cartan lemma 33
Bound along a circle 31
Representation theorems 3(J
THIRD CHAPTER 37
Analytic vector valued functions 37
Subharmonic functions 37
Meromorphic vector valued functions 38
V
vi CONTENTS
Rational functions 40
When is the inverse also meromorphic 42
A simple estimate for matrices 44
FOURTH CHAPTER 47
A product form for matrices 47
Singular value decomposition 50
Basic inequalities for singular values and eigenvalues 51
The total logarithmic size of a matrix 54
Some basic properties of the total logarithmic size 56
Direct sum, Kronecker product and Hadamard product 60
FIFTH CHAPTER 63
The total logarithmic size is subharmonic 63
Behavior near poles 65
Introducing T\ for matrix valued functions 68
Basic identity for inversion 69
Extension to trace class 70
How to work outside the trace class 71
SIXTH CHAPTER 73
Perturbation results 73
Special results for resolvents 77
Powers and their resolvents 79
Bounded characteristics 83
What if small perturbation means small in norm 85
SEVENTH CHAPTER 87
Combining a scalar function with an operator 87
Representing F as G/g 93
Representations for the resolvent 94
Decay of spectral polynomials 96
Robust bounds for Krylov solvers 98
A bound for spectral projectors 100
EIGHTH CHAPTER 103
Approximate polynomial degree of an analytic function 103
Some properties of the approximate polynomial degree 106
Approximate rational degree of a meromorphic function 108
Spijker's lemma 112
Power bounded operators and bounds for the Laurent coefficients 114
NINTH CHAPTER 117
Growth of associated scalar functions 117
Locally algebraic and locally almost algebraic operators 121
TENTH CHAPTER 125
Exceptional values 125
Simple asymptotics for resolvents of matrices 126
Eigenvalues and exceptional values 128
Deficient operators 131
CONTENTS vii
EPILOGUE 133
Lecturing and typing in Toronto 133
Fishing and finishing in Karjalohja 133
BIBLIOGRAPHY 135 |
| any_adam_object | 1 |
| author | Nevanlinna, Olavi 1948- |
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| classification_rvk | SK 700 SK 750 |
| ctrlnum | (OCoLC)51241993 (DE-599)BVBBV015771861 |
| dewey-full | 515/.982 515.982 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.982 515.982 |
| dewey-search | 515/.982 515.982 |
| dewey-sort | 3515 3982 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV015771861 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-20T00:34:38Z |
| institution | BVB |
| isbn | 0821832476 9780821832479 |
| language | English |
| lccn | 2002041519 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010125062 |
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| physical | x, 136 Seiten |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | American Mathematical Society |
| record_format | marc |
| series2 | Fields Institute Monographs / Fields Institute for Research in Mathematical Sciences |
| spelling | Nevanlinna, Olavi 1948- Verfasser (DE-588)1145484786 aut Meromorphic functions and linear algebra Olavi Nevanlinna Providence, Rhode Island American Mathematical Society [2003] © 2003 x, 136 Seiten txt rdacontent n rdamedia nc rdacarrier Fields Institute Monographs / Fields Institute for Research in Mathematical Sciences 18 Aus dem Vorwort: "This monograph is based on lectures which were given in two phases. In the fall of 1995 I gave a series of lectures at the Helsinki University of Technology and in October 2001 at the Fields Institute in Toronto." Algèbre linéaire Fonctions méromorphes Algebras, Linear Functions, Meromorphic Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Meromorphe Funktion (DE-588)4136862-9 gnd rswk-swf Meromorphe Funktion (DE-588)4136862-9 s Lineare Algebra (DE-588)4035811-2 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-3145-7 Fields Institute for Research in Mathematical Sciences Fields Institute Monographs 18 (DE-604)BV009737926 18 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010125062&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nevanlinna, Olavi 1948- Meromorphic functions and linear algebra Algèbre linéaire Fonctions méromorphes Algebras, Linear Functions, Meromorphic Lineare Algebra (DE-588)4035811-2 gnd Meromorphe Funktion (DE-588)4136862-9 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4136862-9 |
| title | Meromorphic functions and linear algebra |
| title_auth | Meromorphic functions and linear algebra |
| title_exact_search | Meromorphic functions and linear algebra |
| title_full | Meromorphic functions and linear algebra Olavi Nevanlinna |
| title_fullStr | Meromorphic functions and linear algebra Olavi Nevanlinna |
| title_full_unstemmed | Meromorphic functions and linear algebra Olavi Nevanlinna |
| title_short | Meromorphic functions and linear algebra |
| title_sort | meromorphic functions and linear algebra |
| topic | Algèbre linéaire Fonctions méromorphes Algebras, Linear Functions, Meromorphic Lineare Algebra (DE-588)4035811-2 gnd Meromorphe Funktion (DE-588)4136862-9 gnd |
| topic_facet | Algèbre linéaire Fonctions méromorphes Algebras, Linear Functions, Meromorphic Lineare Algebra Meromorphe Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010125062&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009737926 |
| work_keys_str_mv | AT nevanlinnaolavi meromorphicfunctionsandlinearalgebra |