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). |
Tartalomjegyzék
Chapter | 1 |
Linear forms and the adjoint space | 10 |
3 Linear operators | 16 |
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adjoint algebraic assume Banach space basis belongs boundary condition bounded operators Cauchy sequence closable closed linear manifold coefficients commutes complete complex numbers consider continuous function convergence denoted densely defined diagonable differential operator dist domain easily seen eigen eigenprojections eigenvalues of T(x eigenvectors elements Example exceptional point exists finite finite-dimensional follows given H₁ Hence Hilbert space holomorphic implies inequality integral operator inverse Lemma linear form linear operator M₂ matrix multiplicity N-tuple nonnegative normed space orthogonal projection orthonormal family P₁ P₂ perturbation Problem proof proved relatively bounded Remark repeated eigenvalues satisfied sectorial selfadjoint semi-Fredholm semilinear form sesquilinear form Similarly space H spectral spectrum subset subspace suffices symmetric operator T-bounded T₁ T₂ Theorem true u₁ unitary space vector space zero