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Topics in Real and Functional Analysis by Gerald Teschl is a book available to read on EtoBox.

What is Topics in Real and Functional Analysis about?

Contents 4 Preface 10 Part 1. Functional Analysis 16 Chapter 1. A first look at Banach and Hilbert spaces 18 1.1. Introduction: Linear partial differential equations 18 1.2. The Banach space of continuous functions 22 1.3. The geometry of Hilbert spaces 32 1.4. Completeness 38 1.5. Compactness 39 1.6. Bounded operators 42 1.7. Sums and quotients of Banach spaces 48 1.8. Spaces of continuous and differentiable functions 51 Chapter 2. Hilbert spaces 56 2.1. Orthonormal bases 56 2.2. The projection theorem and the Riesz lemma 63 2.3. Operators defined via forms 65 2.4. Orthogonal sums and tensor products 70 2.5. Applications to Fourier series 73 Chapter 3. Compact operators 78 3.1. Compact operators 78 3.2. The spectral theorem for compact symmetric operators 81 3.3. Applications to Sturm–Liouville operators 87 3.4. Estimating eigenvalues 95 3.5. Singular value decomposition of compact operators 98 3.6. Hilbert–Schmidt and trace class operators 102 Chapter 4. The main theorems about Banach spaces 110 4.1. The Baire theorem and its consequences 110 4.2. The Hahn–Banach theorem and its consequences 121 4.3. The adjoint operator 129 4.4. Weak convergence 135 4.5. Applications to minimizi

Author

Gerald Teschl

Language

EN