Meromorphic functions and linear algebra / Olavi Nevanlinna.

Format:

Book

Author/Creator:

Nevanlinna, Olavi, 1948-

Series:

Fields Institute monographs 1069-5273 ; 18.

Fields Institute monographs, 1069-5273 ; 18

Language:

English

Subjects (All):

Functions, Meromorphic.

Algebras, Linear.

Physical Description:

x, 136 pages : illustrations ; 26 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, [2003]

Contents:

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

Resolvent 15

Cauchy-integral 20

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 34

Representation theorems 36

Analytic vector valued functions 37

Subharmonic functions 37

Meromorphic vector valued functions 38

Rational functions 40

When is the inverse also meromorphic 42

A simple estimate for matrices 44

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

The total logarithmic size is subharmonic 63

Behavior near poles 65

Introducing T[subscript 1] for matrix valued functions 68

Basic identity for inversion 69

Extension to trace class 70

How to work outside the trace class 71

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

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

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

Growth of associated scalar functions 117

Locally algebraic and locally almost algebraic operators 121

Exceptional values 125

Simple asymptotics for resolvents of matrices 126

Eigenvalues and exceptional values 128

Deficient operators 131

Lecturing and typing in Toronto 133

Fishing and finishing in Karjalohja 133.

Notes:

Includes bibliographical references (pages 135-136).

ISBN:

0821832476

OCLC:

51241993