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Theory of Linear Operators ...
<DIV><DIV>This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.</DIV></DIV>
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Rebiun38947973
https://catalogo.rebiun.org/rebiun/record/Rebiun38947973
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AU-PeEL
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515/.733
Akhiezer, N. I.
Theory of Linear Operators in Hilbert Space
1st ed
Newburyport
Dover Publications
2013
Newburyport
Newburyport
Dover Publications
1 online resource (727 p.)
1 online resource (727 p.)
Text
txt
computer
c
online resource
cr
Dover Books on Mathematics
Description based upon print version of record
Cover; Title Page; Copyright Page; Table of Contents; Theory of Linear Operators in Hilbert Space: Volume I; Chapter I. Hilbert Space; 1. Linear Spaces; 2. The Scalar Product; 3. Some Topological Concepts; 4. Hilbert Space; 5. Linear Manifolds and Subspaces; 6. The Distance from a Point to a Subspace; 7. Projection of a Vector on a Subspace; 8. Orthogonalization of a Sequence of Vectors; 9. Complete Orthonormal Systems; 10. The Space L2; 11. Complete Orthonormal Systems in L2; 12. The Space; 13. The Space of Almost Periodic Functions
Chapter II. Linear Functionals and Bounded Linear Operators14. Point Functions; 15. Linear Functionals; 16. The Theorem of F. Riesz; 17. A Criterion for the Closure in H of a Given System of Vectors; 18. A Lemma Concerning Convex Functionals; 19. Bounded Linear Operators; 20. Bilinear Functionals; 21. The General Form of a Bilinear Functional; 22. Adjoint Operators; 23. Weak Convergence in H; 24. Weak Compactness; 25. A Criterion for the Boundedness of an Operator; 26. Linear Operators in a Separable Space; 27. Completely Continuous Operators
28. A Criterion for Complete Continuity of an Operator29. Sequences of Bounded Linear Operators; Chapter III. Projection Operators and Unitary Operators; 30. Definition of a Projection Operator; 31. Properties of Projection Operators; 32. Operations Involving Projection Operators; 33. Monotone Sequences of Projection Operators; 34. The Aperture of Two Linear Manifolds; 35. Unitary Operators; 36. Isometric Operators; 37. The Fourier-Plancherel Operator; Chapter IV. General Concepts and Propositions in The Theory of Linear Operators; 38. Closed Operators
39. The General Definition of an Adjoint Operator40. Eigenvectors, Invariant Subspaces and Reducibility of Linear Operators; 41. Symmetric Operators; 42. More about Isometric and Unitary Operators; 43. The Concept of the Spectrum (Particularly of a Self-Adjoint Operator); 44. The Resolvent; 45. Conjugation Operators; 46. The Graph of an Operator; 47. Matrix Representations of Unbounded Symmetric Operators; 48. The Operation of Multiplication by the Independent Variable; 49. A Differential Operator; 50. The Inversion of Singular Integrals
Chapter V. Spectral Analysis of Completely Continuous Operators51. A Lemma; 52. Properties of the Eigenvalues of Completely Continuous Operators in R; 53. Further Properties of Completely Continuous Operators; 54. The Existence Theorem for Eigenvectors of Completely Self-Adjoint Operators; 55. The Spectrum of a Completely Continuous Self-Adjoint Operator in R; 56. Completely Continuous Normal Operators; 57. Applications to the Theory of Almost Periodic Functions; Bibliography; Index; Theory of Linear Operators in Hilbert Space: Volume II; Table of Contents
Chapter VI. The Spectral Analysis of Unitary and Self-Adjoint Operators