## I: Functional AnalysisThis 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. |

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### Contents

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 | |

### Other editions - View all

Methods of Modern Mathematical Physics: Functional analysis, Volume 1 Michael Reed,Barry Simon No preview available - 1980 |

### Common terms and phrases

adjoint algebra analytic Baire Banach space Borel measure bounded linear bounded operators bounded self-adjoint operator called Cauchy Chapter closed compact operators complete continuous function Corollary countable deﬁned Deﬁnition Let denote dense discussion domain dual eigenvalue equations equivalent ergodic essentially self-adjoint example exists extend ﬁnd ﬁrst ﬁxed point Fourier transform function f functional calculus given Hausdorff Hilbert space implies inﬁnite inner product integral isometry isomorphic Lebesgue measure 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 reﬂexive satisﬁes Section self-adjoint operator seminorms sequence space 9 spectral theorem spectrum subset subspace Suppose theory topological space unique unitary vector space weak topology weakly zero