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Applied functional analysis. (English) Zbl 0461.46001
Ellis Horwood Series in Mathematics and its Applications. Chichester: Ellis Horwood Limited, Publishers. New York etc.: Halsted Press: a division of John Wiley & Sons. 386 p. £25.00 (1981).

##### MSC:
 46-01 Textbooks (functional analysis) 46C05 Hilbert and pre-Hilbert spaces: geometry and topology 46F05 Topological linear spaces of test functions, distributions and ultradistributions 46B03 Isomorphic theory (including renorming) of Banach spaces 46B10 Duality and reflexivity in normed spaces 46E15 Banach spaces of continuous, differentiable or analytic functions 46E20 Hilbert spaces of continuous, differentiable or analytic functions 46E30 Spaces of measurable functions 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 46F10 Operations with distributions (generalized functions) 46F12 Integral transforms in distribution spaces 47A05 General theory of linear operators 47A10 Spectrum and resolvent of linear operators 47A53 (Semi-)Fredholm operators; index theories 47A70 Eigenfunction expansions of linear operators; rigged Hilbert spaces 47B06 Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers etc.of operators 47B38 Operators on function spaces (general) 47D03 (Semi)groups of linear operators 47E05 Ordinary differential operators 47F05 Partial differential operators 47Gxx Integral, integro-differential, and pseudodifferential operators 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 47J05 Equations involving nonlinear operators (general) 47J25 Iterative procedures (nonlinear operator equations) 49R50 Variational methods for eigenvalues of operators (MSC2000) 34A30 Linear ODE and systems, general 34A35 ODE of infinite order 34L99 Ordinary differential operators 34C15 Nonlinear oscillations, coupled oscillators (ODE) 34D99 Stability theory of ODE 34E99 Asymptotic theory of ODE 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35A08 Fundamental solutions of PDE 35A15 Variational methods (PDE) 35A22 Transform methods (PDE) 35B32 Bifurcation (PDE) 35B35 Stability of solutions of PDE 35C20 Asymptotic expansions of solutions of PDE 35E05 Fundamental solutions (PDE with constant coefficients) 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation 35K05 Heat equation 35L05 Wave equation (hyperbolic PDE) 35J15 Second order elliptic equations, general 35J20 Second order elliptic equations, variational methods 35J30 Higher order elliptic equations, general 35J35 Higher order elliptic equations, variational problems 35P05 General topics in linear spectral theory of PDE 42A16 Fourier coefficients, special Fourier series, etc. 42A20 Convergence and absolute convergence of Fourier and trigonometric series 42A65 Completeness of sets of functions 42B05 Fourier series and coefficients, several variables 45B05 Fredholm integral equations 45C05 Eigenvalue problems (integral equations) 45D05 Volterra integral equations 45G10 Nonsingular nonlinear integral equations 70J25 Stability of linear oscillatory motions 70K20 Stability of nonlinear oscillations (general mechanics) 70K30 Nonlinear resonances (general mechanics) 37G99 Local and nonlocal bifurcation theory 76R99 Diffusion and convection (fluid mechanics) 76U05 Rotating fluids