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Difference equations in normed spaces [[electronic resource] ] : stability and oscillations / / M.I. Gil'
| Difference equations in normed spaces [[electronic resource] ] : stability and oscillations / / M.I. Gil' |
| Autore | Gil' M. I (Mikhail Iosifovich) |
| Pubbl/distr/stampa | Amsterdam ; ; Oxford, : Elsevier, 2007 |
| Descrizione fisica | 1 online resource (379 p.) |
| Disciplina | 515.625 |
| Collana | North-Holland mathematics studies |
| Soggetto topico |
Difference equations
Normed linear spaces |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-75184-3
9786610751846 0-08-046935-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Copyright Page; Preface; Table of Contents; Chapter 1 Definitions and Preliminaries; 1.1 Banach and Hilbert spaces; 1.2 Examples of normed spaces; 1.3 Linear operators; 1.4 Examples of difference equations; 1.5 Stability notions; 1.6 The comparison principle; 1.7 Liapunov functions; 1.8 Ordered spaces and Banach lattices; 1.9 The Abstract Gronwall Lemma; 1.10 Discrete inequalities in a Banach lattice; Chapter 2 Classes of Operators; 2.1 Classification of spectra; 2.2 Compact operators in a Hilbert space; 2.3 Compact matrices; 2.4 Integral operators
Chapter 3 Functions of Finite Matrices3.1 Matrix-valued functions; 3.2 Estimates for the resolvent; 3.3 Examples; 3.4 Estimates for regular matrix functions; 3.5 Proof of Theorem 3.2.4; 3.6 Proofs of Theorems 3.2.1 and 3.2.3; 3.7 Proof of Theorem 3.4.1; 3.8 Non-Euclidean norms of powers of matrices; 3.9 Absolute values of matrix functions; 3.10 Proof of Theorem 3.9.1; Chapter 4 Norm Estimates for Operator Functions; 4.1 Regular operator functions; 4.2 Functions of Hilbert-Schmidt operators; 4.3 Operators with Hilbert-Schmidt powers; 4.4 Resolvents of Neumann-Schatten operators 4.5 Functions of quasi-Hermitian operators4.6 Functions of quasiunitary operators; 4.7 Auxiliary results; 4.8 Equalities for eigenvalues; 4.9 Proofs of Theorems 4.2.1, 4.2.2 and 4.4.1; Chapter 5 Spectrum Perturbations; 5.1 Roots of algebraic equations; 5.2 Roots of functional equations; 5.3 Spectral variations; 5.4 Perturbations of Hilbert-Schmidt operators; 5.5 Perturbations of Neumann - Schatten operators; 5.6 Perturbations of quasi-Hermitian operators; 5.7 Perturbations of finite matrices; Chapter 6 Linear Equations with Constant Operators; 6.1 Homogeneous equations in a Banach space 6.2 Nonhomogeneous equations with constant operators6.3 Perturbations of autonomous equations; 6.4 Equations with Hilbert-Schmidt operators; 6.5 Equations with Neumann-Schatten operators; 6.6 Equations with non-compact operators; 6.7 Equations in finite dimensional spaces; 6.8 Z-transform; 6.9 Exponential dichotomy; 6.10 Equivalent norms in a Banach space; Chapter 7 Liapunov's Type Equations; 7.1 Solutions of Liapunov's type equations; 7.2 Bounds for solutions of Liapunov's type equations; 7.3 Equivalent norms in a Hilbert space; 7.4 Particular cases; Chapter 8 Bounds for Spectral Radiuses 8.1 Preliminary results8.2 Hille - Tamarkin matrices; 8.3 Proof of Theorem 8.2.1; 8.4 Lower bounds for spectral radiuses; 8.5 Finite matrices; 8.6 General operator and block matrices; 8.7 Operator matrices "close" to triangular ones; 8.8 Proof of Theorem 8.7.1; 8.9 Operator matrices with normal entries; 8.10 Scalar integral operators; 8.11 Matrix integral operators; Chapter 9 Linear Equations with Variable Operators; 9.1 Evolution operators; 9.2 Stability conditions; 9.3 Perturbations of evolution operators; 9.4 Equations "close" to autonomous; 9.5 Linear equations with majorants Chapter 10 Linear Equations with Slowly Varying Coefficients |
| Record Nr. | UNINA-9910457217403321 |
Gil' M. I (Mikhail Iosifovich)
|
||
| Amsterdam ; ; Oxford, : Elsevier, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Difference equations in normed spaces [[electronic resource] ] : stability and oscillations / / M.I. Gil'
| Difference equations in normed spaces [[electronic resource] ] : stability and oscillations / / M.I. Gil' |
| Autore | Gil' M. I (Mikhail Iosifovich) |
| Pubbl/distr/stampa | Amsterdam ; ; Oxford, : Elsevier, 2007 |
| Descrizione fisica | 1 online resource (379 p.) |
| Disciplina | 515.625 |
| Collana | North-Holland mathematics studies |
| Soggetto topico |
Difference equations
Normed linear spaces |
| ISBN |
1-280-75184-3
9786610751846 0-08-046935-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Copyright Page; Preface; Table of Contents; Chapter 1 Definitions and Preliminaries; 1.1 Banach and Hilbert spaces; 1.2 Examples of normed spaces; 1.3 Linear operators; 1.4 Examples of difference equations; 1.5 Stability notions; 1.6 The comparison principle; 1.7 Liapunov functions; 1.8 Ordered spaces and Banach lattices; 1.9 The Abstract Gronwall Lemma; 1.10 Discrete inequalities in a Banach lattice; Chapter 2 Classes of Operators; 2.1 Classification of spectra; 2.2 Compact operators in a Hilbert space; 2.3 Compact matrices; 2.4 Integral operators
Chapter 3 Functions of Finite Matrices3.1 Matrix-valued functions; 3.2 Estimates for the resolvent; 3.3 Examples; 3.4 Estimates for regular matrix functions; 3.5 Proof of Theorem 3.2.4; 3.6 Proofs of Theorems 3.2.1 and 3.2.3; 3.7 Proof of Theorem 3.4.1; 3.8 Non-Euclidean norms of powers of matrices; 3.9 Absolute values of matrix functions; 3.10 Proof of Theorem 3.9.1; Chapter 4 Norm Estimates for Operator Functions; 4.1 Regular operator functions; 4.2 Functions of Hilbert-Schmidt operators; 4.3 Operators with Hilbert-Schmidt powers; 4.4 Resolvents of Neumann-Schatten operators 4.5 Functions of quasi-Hermitian operators4.6 Functions of quasiunitary operators; 4.7 Auxiliary results; 4.8 Equalities for eigenvalues; 4.9 Proofs of Theorems 4.2.1, 4.2.2 and 4.4.1; Chapter 5 Spectrum Perturbations; 5.1 Roots of algebraic equations; 5.2 Roots of functional equations; 5.3 Spectral variations; 5.4 Perturbations of Hilbert-Schmidt operators; 5.5 Perturbations of Neumann - Schatten operators; 5.6 Perturbations of quasi-Hermitian operators; 5.7 Perturbations of finite matrices; Chapter 6 Linear Equations with Constant Operators; 6.1 Homogeneous equations in a Banach space 6.2 Nonhomogeneous equations with constant operators6.3 Perturbations of autonomous equations; 6.4 Equations with Hilbert-Schmidt operators; 6.5 Equations with Neumann-Schatten operators; 6.6 Equations with non-compact operators; 6.7 Equations in finite dimensional spaces; 6.8 Z-transform; 6.9 Exponential dichotomy; 6.10 Equivalent norms in a Banach space; Chapter 7 Liapunov's Type Equations; 7.1 Solutions of Liapunov's type equations; 7.2 Bounds for solutions of Liapunov's type equations; 7.3 Equivalent norms in a Hilbert space; 7.4 Particular cases; Chapter 8 Bounds for Spectral Radiuses 8.1 Preliminary results8.2 Hille - Tamarkin matrices; 8.3 Proof of Theorem 8.2.1; 8.4 Lower bounds for spectral radiuses; 8.5 Finite matrices; 8.6 General operator and block matrices; 8.7 Operator matrices "close" to triangular ones; 8.8 Proof of Theorem 8.7.1; 8.9 Operator matrices with normal entries; 8.10 Scalar integral operators; 8.11 Matrix integral operators; Chapter 9 Linear Equations with Variable Operators; 9.1 Evolution operators; 9.2 Stability conditions; 9.3 Perturbations of evolution operators; 9.4 Equations "close" to autonomous; 9.5 Linear equations with majorants Chapter 10 Linear Equations with Slowly Varying Coefficients |
| Record Nr. | UNINA-9910784599903321 |
|
Gil' M. I (Mikhail Iosifovich)
|
||
| Amsterdam ; ; Oxford, : Elsevier, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Difference equations in normed spaces : stability and oscillations / / M.I. Gil'
| Difference equations in normed spaces : stability and oscillations / / M.I. Gil' |
| Autore | Gil' M. I (Mikhail Iosifovich) |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Amsterdam ; ; Oxford, : Elsevier, 2007 |
| Descrizione fisica | 1 online resource (379 p.) |
| Disciplina | 515.625 |
| Collana | North-Holland mathematics studies |
| Soggetto topico |
Difference equations
Normed linear spaces |
| ISBN |
1-280-75184-3
9786610751846 0-08-046935-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Copyright Page; Preface; Table of Contents; Chapter 1 Definitions and Preliminaries; 1.1 Banach and Hilbert spaces; 1.2 Examples of normed spaces; 1.3 Linear operators; 1.4 Examples of difference equations; 1.5 Stability notions; 1.6 The comparison principle; 1.7 Liapunov functions; 1.8 Ordered spaces and Banach lattices; 1.9 The Abstract Gronwall Lemma; 1.10 Discrete inequalities in a Banach lattice; Chapter 2 Classes of Operators; 2.1 Classification of spectra; 2.2 Compact operators in a Hilbert space; 2.3 Compact matrices; 2.4 Integral operators
Chapter 3 Functions of Finite Matrices3.1 Matrix-valued functions; 3.2 Estimates for the resolvent; 3.3 Examples; 3.4 Estimates for regular matrix functions; 3.5 Proof of Theorem 3.2.4; 3.6 Proofs of Theorems 3.2.1 and 3.2.3; 3.7 Proof of Theorem 3.4.1; 3.8 Non-Euclidean norms of powers of matrices; 3.9 Absolute values of matrix functions; 3.10 Proof of Theorem 3.9.1; Chapter 4 Norm Estimates for Operator Functions; 4.1 Regular operator functions; 4.2 Functions of Hilbert-Schmidt operators; 4.3 Operators with Hilbert-Schmidt powers; 4.4 Resolvents of Neumann-Schatten operators 4.5 Functions of quasi-Hermitian operators4.6 Functions of quasiunitary operators; 4.7 Auxiliary results; 4.8 Equalities for eigenvalues; 4.9 Proofs of Theorems 4.2.1, 4.2.2 and 4.4.1; Chapter 5 Spectrum Perturbations; 5.1 Roots of algebraic equations; 5.2 Roots of functional equations; 5.3 Spectral variations; 5.4 Perturbations of Hilbert-Schmidt operators; 5.5 Perturbations of Neumann - Schatten operators; 5.6 Perturbations of quasi-Hermitian operators; 5.7 Perturbations of finite matrices; Chapter 6 Linear Equations with Constant Operators; 6.1 Homogeneous equations in a Banach space 6.2 Nonhomogeneous equations with constant operators6.3 Perturbations of autonomous equations; 6.4 Equations with Hilbert-Schmidt operators; 6.5 Equations with Neumann-Schatten operators; 6.6 Equations with non-compact operators; 6.7 Equations in finite dimensional spaces; 6.8 Z-transform; 6.9 Exponential dichotomy; 6.10 Equivalent norms in a Banach space; Chapter 7 Liapunov's Type Equations; 7.1 Solutions of Liapunov's type equations; 7.2 Bounds for solutions of Liapunov's type equations; 7.3 Equivalent norms in a Hilbert space; 7.4 Particular cases; Chapter 8 Bounds for Spectral Radiuses 8.1 Preliminary results8.2 Hille - Tamarkin matrices; 8.3 Proof of Theorem 8.2.1; 8.4 Lower bounds for spectral radiuses; 8.5 Finite matrices; 8.6 General operator and block matrices; 8.7 Operator matrices "close" to triangular ones; 8.8 Proof of Theorem 8.7.1; 8.9 Operator matrices with normal entries; 8.10 Scalar integral operators; 8.11 Matrix integral operators; Chapter 9 Linear Equations with Variable Operators; 9.1 Evolution operators; 9.2 Stability conditions; 9.3 Perturbations of evolution operators; 9.4 Equations "close" to autonomous; 9.5 Linear equations with majorants Chapter 10 Linear Equations with Slowly Varying Coefficients |
| Record Nr. | UNINA-9910810587703321 |
|
Gil' M. I (Mikhail Iosifovich)
|
||
| Amsterdam ; ; Oxford, : Elsevier, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||