Treatise on Analysis

ISBN: 9780122155086 出版年：2016 页码：377 Dieudonne, J Academic Press_RM

Part 1 Weyl-Kodaira theory: elliptical differential operators on an interval of R boundary conditions self-adjoint operators associated with a linear differential equation the case of second order equations example - second order equations with periodic-coefficients example - Gelfand-Levitan equations. Part 2 Multilayer potentials: symbols of rational type the case of hyperplane multilayers general case. Part 3 Fine boundary value problems for elliptical differential operators: the Calderon operator elliptic boundary value problems ellipticity criteria the spaces Hs,r (U+) Hs,r - spaces and P-potentials regularity on the boundary coercive problems generalized Green's formula fine problems associated with coercive problems examples extension to some non-Hermitian operators case of second-order operators Neumann's problem the maximum principle. Part 4 Parabolic equations: construction of one-sided local resolvent the one-sided global Cauchy problem traces and eigenvalues. Part 5 Evolution distributions - the wave equation: generalized Cauchy problem propagation and domain of influence signals, waves and rays. Part 6 Strictly hyperbolic equations: preliminary results construction of a local approximate resolvent examples and variations the Cauchy problem for strictly hyperbolic differential operators existence and local uniqueness global problems extension to manifolds. Part 7 Application to the spectrum of a Hermitian elliptic operator.