Perturbation Theory for Linear OperatorsSpringer-Verlag, 1966 - 592 oldal This book is intended to give a systematic presentation of perturba tion theory for linear operators. It is hoped that the book will be useful to students as well as to mature scientists, both in mathematics and in the physical sciences. Perturbation theory for linear operators is a collection of diversified results in the spectral theory of linear operators, unified more or less loosely by their common concern with the behavior of spectral properties when the operators undergo a small change. Since its creation by RAY LEIGH and SCHRODINGER, the theory has occupied an important place in applied mathematics; during the last decades, it has grown into a mathematical discipline with its own interest. The book aims at a mathe matical treatment of the subject, with due consideration of applications. The mathematical foundations of the theory belong to functional analysis. But since the book is partly intended for physical scientists, who might lack training in functional analysis, not even the elements of that subject are presupposed. The reader is assumed to have only a basic knowledge of linear algebra and real and complex analysis. The necessary tools in functional analysis, which are restricted to the most elementary part of the subject, are developed in the text as the need for them arises (Chapters I, III and parts of Chapters V, VI). |
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Chapter | 1 |
Vectorvalued functions | 8 |
The convexity of balls | 14 |
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adjoint analytic assume Banach space belongs boundary condition bounded operator bounded-holomorphic Cauchy sequence closable closed linear manifold closure coefficients commutes compact resolvent complete complex numbers consider continuous convergence denote densely defined differential operator dist domain eigen eigenprojections eigenvalues of T(x eigenvectors Example exists finite finite-dimensional follows Friedrichs extension function given H₁ H₂ Hence Hilbert space holomorphic family implies inequality integral operator interval inverse isolated eigenvalue Lemma linear operator m-sectorial M₂ matrix multiplicity nonnegative norm orthogonal projection P₁ P₂ perturbation theory Problem proof of Theorem proved PT(¹ R₂ real axis relatively bounded Remark replaced restriction satisfied selfadjoint selfadjoint operator semigroup sense sequence sesquilinear form space H spectral spectrum subset subspace sufficiently symmetric operator T-bounded T₁ T₂ true u₁ unitary unitary space vector zero