Advances in mathematics research. Vol. 16 / Albert R. Baswell, editor.

Includes bibliographical references and index.

Print version record.

ADVANCES IN MATHEMATICS RESEARCH. VOLUME 16; ADVANCES IN MATHEMATICS RESEARCH. VOLUME 16; LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA; CONTENTS; PREFACE; Chapter 1: BLACKWELL'S ORDERING IN THE SEMIRING OF MONOTONE DOUBLY STOCHASTIC MATRICES; Abstract; 1. Introduction; 2. Preliminaries; 2.1. Homogenous Markov Chains; 2.2. Monotone Transition Matrices; 2.3. Ordering in an Idempotent Semiring; 3. Measuring Mobility; 3.1. Shorrocks' Mobility Measuring Approach; 3.2. Dardanoni's Mobility Measuring; 4. Ordering in Shorrocks' Sense on the Semiring of Monotone Doubly Stochastic Matrices.

4.1. Semiring of Monotone Doubly Stochastic Matrices4.2. Characterisation of the Ordering f and the Ordering m; 5. Blackwell's Ordering in the Semiring of Monotone Doubly Stochastic Matrices; 6. A comparison of Shorrocks' and Blackwell's Ordering in theSemiring of Monotone Doubly Stochastic Matrices; 6.1. The Relation of Blackwell's Ordering #x9C;́ư and Ordering #x9C;́ư Induced byMobility Measures; 6.2. The Orderings #x9C;́ư, #x9C;́ư and Dardanoni's Ordering; 7. Conclusion; Acknowledgment; References; Chapter 2: ESTIMATES FOR FUNCTIONS OF FINITEAND INFINITE MATRICES. PERTURBATIONS OF MATRIX FUNCTIONS.

Abstract1. Introduction and Notation; 2. Representations of Matrix Functions; 2.1. Classical Representations; 2.2. Multiplicative Representations of the Resolvent; 3. Norm Estimates for Resolvents ; 4. Spectrum Perturbations; 5. Norm Estimates for Matrix Functions Regular on SimplyConnected Sets; 5.1. Estimates via the Resolvent; 5.2. Functions Regular on the Convex Hull of the Spectrum; 5.3. Proof of Theorem 5.2; 6. Estimates for Absolute Values of Entries; 7. Splitting of Spectrum; 7.1. Splitting via the Resolvent; 7.2. Splitting via the Riesz Projections.

7.3. Block Triangular Representation of the Resolvent 8. Derivatives of Matrix Functions; 8.1. Statements of the Results; 8.2. Proof of Theorem 8.1; 8.3. Derivative of Matrix Exponential; 9. MeromorphicMatrix Functions; 9.1. Statements of the Results; 9.2. Proof of Theorem 9.4; 9.3. Periodic Vector Problem ; 9.4. Two-Points Vector Boundary Value Problem; 10. Norm Estimates for Functions of Diagonalizable Matrices ; 10.1. A Bound for Similarity Constants of Matrices ; 10.2. Proof of Theorem 10.1 ; 10.3. Applications of Theorem 10.1.

10.4. Additional Norm Estimates for Functionsof Diagonalizable Matrices11. Perturbations of Functions of Matrices With ArbitrarySpectra; 11.1. Perturbations in Terms of the Spectral Norm; 11.2. Perturbations in Terms of the Frobenius Norm; 11.3. Perturbations of Entries of Matrix Functions; 11.4. Perturbations of Entire Functions; 11.5. Applications of the Derivative; 12. Perturbations of Functions of DiagonalizableMatrices; 13. Matrix Exponential; 13.1. Dichotomy; 13.2. Perturbations of Matrix Exponentials ; 13.3. Proof of Theorem 13.1; 14. Fractional Powers.

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