preface to the third edition preface to the second edition preface to the first edition chapter1 nermed vector spaces 1.1 introduction 1.2 vector spaces 1.3 normed spaces 1.4 knach spaces 1.s linear mappings 1.6 contraction mappings and the banach fixed point theorem 1.7 exercises chapter2 the lebesgue integral 2.1 introduction 2.2 step functions 2.3 lebesl~e intelfable functions
preface to the third edition preface to the second edition preface to the first edition chapter1 nermed vector spaces 1.1 introduction 1.2 vector spaces 1.3 normed spaces 1.4 knach spaces 1.s linear mappings 1.6 contraction mappings and the banach fixed point theorem 1.7 exercises chapter2 the lebesgue integral 2.1 introduction 2.2 step functions 2.3 lebesl~e intelfable functions 2.4 the absolute value of on intei fable function 2.5 series of intelqble functions so 2.6 norm in l1(r) 2.7 convergence almost everywhere ss 2.8 fundamentol convergence theorems 2.9 locally integmble functions 2.10 the lebesgue integral and the riemann integral 2.11 lebesgue measure on r 2.12 complex-valued lebesgue integrable functions 2.13 the spaces lp(r) 2.14 lebesgue integrable functions on rn 2.15 convolution 2.16 exercises chapter3 hilbert spaces and orthonormal systems 3.1 introduction 3.2 inner product spaces 3.3 hilbert spaces 3.4 orthogonal and orthonormal systems 3.5 trigonometric fourier series 3.6 orthogonal complements and projections 3.7 linear functionals and the riesz representation theorem 3.8 exercises chapter4 linear operators on hilbert spaces 4.1 introduction 4.2 examples of operators 4.3 bilinear functionals and quadratic forms 4.4 adjoint and seif-adjoint operators 4.5 invertible, normal, isometric, and unitary operators 4.6 positive operators 4.7 projection operators 4.8 compact operators 4.9 eigenvalues and eigenvectors 4.10 spectral decomposition 4.11 unbounded operators 4.12 exercises chapter5 applications to integral and differential equations 5.1 introduction 5.2 basic existence theorems 5.3 fredholm integral equations 5.4 method of successive approximations 5.5 volterra integral equations 5.6 method of solution for a separable kernel 5.7 volterra integral equations of the first kind and abel'sintegral equation 5.8 ordinary differential equations and differentialoperators 5.9 sturm-liouville systems 5.10 inverse differential operators and green's functions 5.11 the fourier transform 5.12 applications of the fourier transform to ordinarydifferential equations and integral equations 6.13 exercises chapter6 generalized functions and partial differentialequations 6.1 introduction 6.2 distributions 6.3* sobolevspaces 6.4 fundamental solutions and green's functions for partialdifferential equations 6.5 weak solutions of elliptic boundary value problems 6.6 examples of applications of the fourier transform to partialdifferential equations 6.7 exercises chapter7 mathematical foundations of @uantum mechanics 7.1 introduction 7.2 basic concepts and equations of classical mechanics poisson's brackets in mechanics 7.3 basic concepts and postulates of quantum mechanics 7.4 the heisenberg uncertainty principle 7.5 the schrodinger equation of motion 7.6 the schrodinger picture 7.7 the heisenberg picture and the heisenberg equation ofmotion 7.8 the interaction picture 7.9 the linear harmonic oscillator 7.10 angular momentum operators 7.11 the dirac relativistic wave equation 7.12 exercises chapter8 wavelets and wavelet transforms 8.1 brief historical remarks 8.2 continuous wavelet transforms 8.3 the discrete wavelet transform 8.4 multirosolution analysis and orthonormal bases ofwavelets 8.5 examples of orthonormal wavelets 8.6 exercises chapter9 optimization problems and other miscellaneousapplications 9.1 introduction 9.2 the gateaux and frechet differentials 9.3 optimization problems and the euler-lagrange equations 9.4 minimization of quadratic functionals s0s 9.5 variational inequalities s07 9.6 optimal control problems for dynamical systems 9.7 approximation theory 9.8 the shannon samplingtheorem 9.9 linear and nonlinear stability 9.10 bifurcation theory 9.11 exercises hints and answers to selected exercises bibliography index
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