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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:
46-01Textbooks (functional analysis)
46C05Hilbert and pre-Hilbert spaces: geometry and topology
46F05Topological linear spaces of test functions, distributions and ultradistributions
46B03Isomorphic theory (including renorming) of Banach spaces
46B10Duality and reflexivity in normed spaces
46E15Banach spaces of continuous, differentiable or analytic functions
46E20Hilbert spaces of continuous, differentiable or analytic functions
46E30Spaces of measurable functions
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46F10Operations with distributions (generalized functions)
46F12Integral transforms in distribution spaces
47A05General theory of linear operators
47A10Spectrum and resolvent of linear operators
47A53(Semi-)Fredholm operators; index theories
47A70Eigenfunction expansions of linear operators; rigged Hilbert spaces
47B06Riesz operators; eigenvalue distributions; approximation numbers, s-numbers etc.of operators
47B38Operators on function spaces (general)
47D03(Semi)groups of linear operators
47E05Ordinary differential operators
47F05Partial differential operators
47GxxIntegral, integro-differential, and pseudodifferential operators
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47J05Equations involving nonlinear operators (general)
47J25Iterative procedures (nonlinear operator equations)
49R50Variational methods for eigenvalues of operators (MSC2000)
34A30Linear ODE and systems, general
34A35ODE of infinite order
34L99Ordinary differential operators
34C15Nonlinear oscillations, coupled oscillators (ODE)
34D99Stability theory of ODE
34E99Asymptotic theory of ODE
35A05General existence and uniqueness theorems (PDE) (MSC2000)
35A08Fundamental solutions of PDE
35A15Variational methods (PDE)
35A22Transform methods (PDE)
35B32Bifurcation (PDE)
35B35Stability of solutions of PDE
35C20Asymptotic expansions of solutions of PDE
35E05Fundamental solutions (PDE with constant coefficients)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
35K05Heat equation
35L05Wave equation (hyperbolic PDE)
35J15Second order elliptic equations, general
35J20Second order elliptic equations, variational methods
35J30Higher order elliptic equations, general
35J35Higher order elliptic equations, variational problems
35P05General topics in linear spectral theory of PDE
42A16Fourier coefficients, special Fourier series, etc.
42A20Convergence and absolute convergence of Fourier and trigonometric series
42A65Completeness of sets of functions
42B05Fourier series and coefficients, several variables
45B05Fredholm integral equations
45C05Eigenvalue problems (integral equations)
45D05Volterra integral equations
45G10Nonsingular nonlinear integral equations
70J25Stability of linear oscillatory motions
70K20Stability of nonlinear oscillations (general mechanics)
70K30Nonlinear resonances (general mechanics)
37G99Local and nonlocal bifurcation theory
76R99Diffusion and convection (fluid mechanics)
76U05Rotating fluids