Methods of Modern Mathematical Physics: Functional analysis, Volume 1Gulf Professional Publishing, 1980 - 400 pages "This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations." --Publisher description. |
Table des matières
Chapter I PRELIMINARIES | 1 |
Chapter II HILBERT SPACES | 36 |
Chapter III BANACH SPACES | 67 |
Chapter IV TOPOLOGICAL SPACES | 90 |
Chapter V LOCALLY CONVEX SPACES | 124 |
Chapter VI BOUNDED OPERATORS | 182 |
Chapter VII THE SPECTRAL THEOREM | 221 |
Chapter VIII UNBOUNDED OPERATORS | 249 |
THE FOURIER TRANSFORM | 318 |
SUPPLEMENTARY MATERIAL | 344 |
| 393 | |
| 395 | |
Autres éditions - Tout afficher
Methods of Modern Mathematical Physics: Functional analysis Michael Reed,Barry Simon Affichage d'extraits - 1972 |
Methods of Modern Mathematical Physics: Functional analysis, Volume 1 Michael Reed,Barry Simon Affichage d'extraits - 1980 |
Expressions et termes fréquents
adjoint analytic Baire Banach space bounded linear bounded operators bounded self-adjoint operator called Cauchy closed compact operators complete continuous function Corollary countable define Definition Let denote dense discussion domain dual eigenvalue equations equivalent ergodic essentially self-adjoint example extend Fourier transform function f functional calculus given Hausdorff Hausdorff space Hilbert space implies inner product integral isomorphic L²(M L²(R lemma Let f limit linear functional locally convex space Math mathematical measure space metric space multiplication neighborhood normed linear space notion numbers open sets orthogonal orthonormal basis pointwise positive Problem Proof Let proof of Theorem properties Proposition Prove quadratic form resolvent sense Section self-adjoint operator seminorms sequence spectral theorem spectrum subset subspace Suppose T₁ theory topological space uniformly unique unitary vector space weak topology weakly y₁ zero