Applied functional analysis
This introductory text examines many important applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Discusses distribution theory, Green's functions, Banach spaces, Hilbert space, spectral theory, and variational techniques. Also outlines the ideas behind Frechet calculus, stability and bifurcation theory, and Sobolev spaces. 1985 ed. Includes 25 Figures and 9 Appendices. Supplementary Problems. Indexes.
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Differential Equations and Greens Functions
Fourier Transforms and Partial Differential Equations
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algebraic applied approximation Banach space basis bifurcation boundary conditions bounded linear operator bounded set calculation called Cauchy sequence Chapter coefficients compact operator complete consider continuous function convergent sequence corresponding deduce defined Definition delta function dense derivative differential operator discussed distribution of slow distribution theory easy eigenfunctions eigenvalue problem eigenvectors elements equilibrium equivalent Example finite finite-dimensional spaces follows Fourier transform fundamental solution generalised functions given gives Green's function Hence Hilbert space idea infinite infinite-dimensional inner product space integral equation integral operator interval invertible Lemma linear combination linear functional locally integrable mathematical matrix method nonlinear normed space notation numbers ordinary orthonormal polynomial Proof Proposition prove Rayleigh-Ritz real numbers relatively compact result satisfies scalar self-adjoint operator slow growth space H spectral theorem square-integrable Sturm-Liouville subset subspace symmetric tends to zero test function unique vanishes variables vector space