Introduction to Hilbert spaces with applications
Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, 3E, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory.* Updated chapter on wavelets* Improved presentation on results and proof* Revised examples and updated applications* Completely updated list of references .
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adjoint Banach space bifurcation bilinear functional boundary conditions bounded linear bounded operator called Cauchy sequence classical mechanics commute compact operator complete orthonormal completes the proof complex numbers Consider constant continuous functions convergence corresponding Definition denoted differential equation differential operator distribution eigenfunctions eigenvalue eigenvectors element energy equivalent Example finite dimensional following theorem Fourier transform Frechet derivative given Hence Hilbert space implies inequality inner product space integral equation interval inverse Lebesgue integrable Lemma linear mapping linear operator linearly independent locally integrable function measurable non-zero normed space null set observable operator obtain orthogonal orthonormal sequence orthonormal system particle polynomials positive operator projection operator quantum mechanics real numbers satisfies scalar self-adjoint operator sequence of functions Show space H step functions subset Suppose symmetric test function theory unique solution valued function vanish variables vector space x e H xe H