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001438573 001__ 1438573
001438573 003__ OCoLC
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001438573 019__ $$a1262190653
001438573 020__ $$a9789811625282$$q(electronic bk.)
001438573 020__ $$a981162528X$$q(electronic bk.)
001438573 020__ $$z9789811625275
001438573 020__ $$z9811625271
001438573 0247_ $$a10.1007/978-981-16-2528-2$$2doi
001438573 035__ $$aSP(OCoLC)1262371989
001438573 040__ $$aEBLCP$$beng$$erda$$epn$$cEBLCP$$dYDX$$dGW5XE$$dEBLCP$$dOCLCO$$dOCLCF$$dUKAHL$$dOCLCQ$$dCOM$$dSFB$$dOCLCO$$dOCLCQ
001438573 049__ $$aISEA
001438573 050_4 $$aQA329.2$$b.J47 2021
001438573 08204 $$a515/.7246$$223
001438573 1001_ $$aJeribi, Aref,$$eauthor.
001438573 24510 $$aPerturbation theory for linear operators :$$bdenseness and bases with applications /$$cAref Jeribi.
001438573 264_1 $$aSingapore :$$bSpringer,$$c[2021]
001438573 264_4 $$c©2021
001438573 300__ $$a1 online resource (523 pages) :$$billustrations
001438573 336__ $$atext$$btxt$$2rdacontent
001438573 337__ $$acomputer$$bc$$2rdamedia
001438573 338__ $$aonline resource$$bcr$$2rdacarrier
001438573 504__ $$aIncludes bibliographical references and index.
001438573 5050_ $$aIntro -- Preface -- Introduction -- References -- Contents -- About the Author -- Symbols Description -- 1 Basic Notations and Results -- 1.1 Spaces and Operators -- 1.1.1 Vector and Normed Spaces -- 1.1.2 Operators on Quasi-Banach Spaces -- 1.1.3 Closed and Closable Operators -- 1.1.4 Adjoint Operator -- 1.1.5 Fredholm Operators -- 1.2 Some Notions of Spectral Theory -- 1.2.1 Closed Graph Theorem -- 1.2.2 Resolvent Set and Spectrum -- 1.2.3 Bounded Operators -- 1.2.4 Numerical Range -- 1.3 Inequalities -- 1.4 Closed Operators -- 1.4.1 Closed Operator Perturbations
001438573 5058_ $$a1.4.2 A-Bounded, A-Closed, and A-Closable -- 1.5 Lebesgue-Dominated Convergence Theorem -- 1.6 Compact, Weakly Compact, Strictly Singular ... -- 1.6.1 Compact Operator -- 1.6.2 Weakly Compact Operator -- 1.6.3 Strictly Singular Operator -- 1.6.4 Discrete Operator -- 1.6.5 Ascent and Descent Operators -- 1.6.6 Riesz Operator -- 1.7 A-Compact Operators -- 1.8 Dunford-Pettis Property -- 1.9 The Jeribi Essential Spectrum -- 1.9.1 Definition -- 1.9.2 A Characterization of the Jeribi Essential Spectrum -- 1.10 Jordan Chain for an Operator and Multiplicities
001438573 5058_ $$a1.11 Laurent Series Expansion of the Resolvent -- 1.12 Bases -- 1.12.1 Algebraic Bases (Hamel Bases) -- 1.12.2 On a Schauder Basis -- 1.13 Normal Operator -- 1.14 Positive Operators -- 1.15 Spectrum of the Sum of Two Operators -- 1.16 Notes and Remarks -- References -- 2 Analysis with Operators -- 2.1 Projections -- 2.1.1 Generalities -- 2.1.2 Orthogonal Projection -- 2.1.3 Spectral Projection -- 2.1.4 Sum of Spectral Projection -- 2.1.5 l2-Decomposition -- 2.2 Spectral Theory of Compact and Discrete Operators -- 2.2.1 Riesz-Schauder Theorem -- 2.2.2 Discrete Operators -- 2.3 Functions
001438573 5058_ $$a2.3.1 Function of Finite Order -- 2.3.2 Function of Sine Type -- 2.3.3 Generating Function in L2(0, T) -- 2.4 Phragmén-Lindelöf Theorems -- 2.5 Holomorphic Operator Functions -- 2.5.1 Spectrum and Multiplicities -- 2.5.2 Zeros of a Holomorphic Function -- 2.5.3 Determinant of Operator -- 2.6 Semigroup Theory -- 2.6.1 Definitions -- 2.6.2 Example -- 2.7 Concepts of Subordination and Fully Subordination -- 2.7.1 Concepts of Subordination -- 2.7.2 Concepts of Fully Subordination -- 2.8 Notes and Remarks -- References -- 3 Series of Complex Terms -- 3.1 Identity Results -- 3.1.1 Technical Results
001438573 5058_ $$a3.1.2 Proof of Eq. (3.0.1) When (ak)k equiv1 -- 3.1.3 General Case -- 3.2 Duality Bracket -- 3.2.1 Proof of Eq. (3.2.1) When (ak)k equiv1 -- 3.2.2 Proof of Eq. (3.2.1) When (ak)k1 is Any Sequence in mathbbC -- 3.3 Notes and Remarks -- References -- 4 Carleman-Class -- 4.1 Singular Values -- 4.1.1 Singular Values of a Compact Operator -- 4.1.2 Polar Representation of a Bounded Operator -- 4.1.3 The Dimension of an Operator -- 4.1.4 The Schmidt Expansion of a Compact Operator -- 4.1.5 Some Properties of Singular Values -- 4.1.6 Intermediate Ideals Between F(X) and mathcalK(X)
001438573 506__ $$aAccess limited to authorized users.
001438573 520__ $$aThis book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with the completeness of the space of generalized eigenvectors, bases on Hilbert and Banach spaces and asymptotic behavior of the eigenvalues of these operators. Most results in the book are motivated by physical problems, such as the perturbation method for sound radiation by a vibrating plate in a light fluid, Gribov operator in Bargmann space and other applications in mathematical physics and mechanics. This book is intended for students, researchers in the field of spectral theory of linear non self-adjoint operators, pure analysts and mathematicians.
001438573 588__ $$aDescription based on print version record.
001438573 650_0 $$aSpectral theory (Mathematics)
001438573 650_0 $$aLinear operators.
001438573 650_0 $$aPerturbation (Mathematics)
001438573 650_6 $$aSpectre (Mathématiques)
001438573 650_6 $$aOpérateurs linéaires.
001438573 650_6 $$aPerturbation (Mathématiques)
001438573 655_7 $$aLlibres electrònics.$$2thub
001438573 655_0 $$aElectronic books.
001438573 77608 $$iPrint version:$$aJeribi, Aref.$$tPerturbation Theory for Linear Operators.$$dSingapore : Springer Singapore Pte. Limited, ©2021$$z9789811625275
001438573 852__ $$bebk
001438573 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-16-2528-2$$zOnline Access$$91397441.1
001438573 909CO $$ooai:library.usi.edu:1438573$$pGLOBAL_SET
001438573 980__ $$aBIB
001438573 980__ $$aEBOOK
001438573 982__ $$aEbook
001438573 983__ $$aOnline
001438573 994__ $$a92$$bISE