現(xiàn)代數(shù)學(xué)物理方法（第1卷）

內(nèi)容概要

　　This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modem 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, modem physics, and partial differenrial equations.

書(shū)籍目錄

Preface Introduction Contents of Other Volumes I: PRELIMINARIES 　1. Sets and functions 　2. Metric and normed linear spaces 　　Appendix Lira sup and lim inf 　3. The Lebesgue integral 　4. Abstract measure theory 　5. Two conrergence arguments 　6. Equicontinuity 　Notes 　Problems II: HILBERT SPACES 　1. The geometry of Hilbert space 　2. The Riesz lemma 　3. Orthonormal bases 　4. Tensor products of Hilbert spaces 　5. Ergodic theory: an introduction 　Notes 　ProblemsIII:　BANACH　SPACES　1. Definition　and　examples　2. Duals　and　double　duals　3. The　Hahn-Banach　theorem　4. Operations　on　Banach　spaces　5. The　Baire category　theorem　and　its　consequences　Notes　ProblemsIV:　TOPOLOGICAL　SPACES　1. General　notions　2. Nets　and　Convergence　3. Compactness　　Appendix The　Stone-Weierstrass　theorem　4. Measure　theory　on Compact　spaces　5. Weak　topologies　on　Banach　spaces　Appendix Weak　and　strong　measurability　Notes　ProblemsV: LOCALLY ONVEX　SPACES　1. General　properties　2. Frdchet　spaces　3. Functions　of　rapid　decease　and　the　tempered　distributions　　Appendix The　N-representation　for　and　4. Inductive　limits:　generalized　functions　and　weak　solutions　of partial　differential　equations　5. Fixed　point　theorems　6. Applications　of　fixed　point　theorems　7. Topologies　on　locally　convex　spaces:　duality　theory　and　the strong　dual　topology　　　Appendix Polars　and　the　Mackey-Arens　theorem　Notes　ProblemsVI: BOUNDED　OPERATORSVII: THE　SPECTRAL　THEOREMVIII: UNBOUNDED　OPERATORSTHE　FOURIER　TRANSFORMSUPPLEMENTARY　MATERIALList　of　Symbols

編輯推薦

This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modem 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, modem physics, and partial differenrial equations.

圖書(shū)封面

圖書(shū)標(biāo)簽Tags

無(wú)

評(píng)論、評(píng)分、閱讀與下載

---

    現(xiàn)代數(shù)學(xué)物理方法（第1卷） PDF格式下載

---