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Algebraic Multiplicity of Eigenvalues of Linear Operators

Part of the Operator Theory: Advances and Applications Book Series (volume 177)

DOI: 10.1007/978-3-7643-8401-2

ISBN: 978-3-7643-8400-5

Publisher: Birkhäuser Basel - Springer Journals

Jan 1, 2007

1 - 10 of 12 Chapters

LitStream

The Jordan Theorem

Pages: 3 –35

[In this chapter we prove the Jordan theorem, a pivotal result in mathematics, which establishes that, for every \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
LitStream

Operator Calculus

Pages: 37 –62

[In Section 1.2 we defined P(A) when P is a polynomial and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Spectral Projections

Pages: 63 –73

[This chapter considers \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ A \in...
LitStream

Algebraic Multiplicity Through Transversalization

Pages: 83 –106

[Throughout this chapter we will consider \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
LitStream

Algebraic Multiplicity Through Polynomial Factorization

Pages: 107 –137

[This chapter describes an equivalent approach to the concept of multiplicity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Uniqueness of the Algebraic Multiplicity

Pages: 139 –152

[Throughout this chapter, given \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
LitStream

Algebraic Multiplicity Through Jordan Chains. Smith Form

Pages: 153 –207

[This chapter studies the algebraic multiplicity according to the theory of Jordan chains. The concept of Jordan chain extends the classic concept of chain of generalized eigenvectors, already studied in Section 1.3. It will provide us with a further approach to the algebraic multiplicities χ and...
LitStream

Analytic and Classical Families. Stability

Pages: 209 –223

[This chapter focuses attention on the analytic operator families. After studying some universal spectral properties of these families, this chapter deals with the classical families \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}...
LitStream

Algebraic Multiplicity Through Logarithmic Residues

Pages: 225 –247

[The stability results of Section 8.4 can be regarded as infinite-dimensional versions of the classic Rouché theorem. A closely related topic in complex function theory is the so-called argument principle, otherwise known as the logarithmic residue theorem, which has been established by Theorem...
LitStream

The Spectral Theorem for Matrix Polynomials

Pages: 249 –264

[This chapter studies the polynomial families of the form 10.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...

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