preface to the third editionpreface to the second editionpreface to the first editionchapter1 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 exerciseschapter2 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 exerciseschapter3 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 exerciseschapter4 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 exerciseschapter5 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's integral equation 5.8 ordinary differential equations and differential operators 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 ordinary differential equations and integral equations 6.13 exerciseschapter6 generalized functions and partial differential equations 6.1 introduction 6.2 distributions 6.3* sobolevspaces 6.4 fundamental solutions and green's functions for partial differential equations 6.5 weak solutions of elliptic boundary value problems 6.6 examples of applications of the fourier transform to partial differential equations 6.7 exerciseschapter7 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 of motion 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 exerciseschapter8 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 of wavelets 8.5 examples of orthonormal wavelets 8.6 exerciseschapter9 optimization problems and other miscellaneous applications 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 exerciseshints and answers to selected exercisesbibliographyindex
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