| 1 Preliminaries 1.1 Linear Algebra 1.2 Metric Spaces 1.3 Lebesgue Integration 2 Normed Spaces 2.1 Examples of Normed Spaces 2.2 Finite-dimensional Normed Spaces 2.3 Banach Spaces 3 Inner Product Spaces, Hilbert Spaces 3.1 Inner Products 3.2 Orthogonality 3.3 Orthogonal Complements 3.4 Orthonormal Bases in Infinite Dimensions 3.5 Fourier Series 4 Linear Operators 4.1 Continuous Linear Transformations 4.2 The Norm of a Bounded Linear Operator 4.3 The Space B(X,Y) and Dual Spaces 4.4 Inverses of Operators 5 Linear Operators on Hilbert Spaces 5.1 The Adjoint of an Operator 5.2 Normal, Self-adjoint and Unitary Operators 5.3 The Spectrum of an Operator 5.4 Positive Operators and Projections 6 Compact Operators 6.1 Compact Operators 6.2 Spectral Theory of Compact Operators 6.3 Self-adjoint Compact Operators 7 Integral and Differential Equations 7.1 Fredholm Integral Equations 7.2 Volterra Integral Equations 7.3 Differential Equations 7.4 Eigenvalue Problems and Green's Functions 8 Solutions to Exercises Further Reading References Notation Index Index |
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