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MSC 2000:

*47-02 Research monographs (operator theory)
47B15 Hermitian and normal operators
47F05 Partial differential operators
47B25 Symmetric and selfadjoint operators (unbounded)
46J05 General theory of commutative topological algebras
22B05 General properties and structure of LCA groups
47D03 (Semi)groups of linear operators
47E05 Ordinary differential operators
47A10 Spectrum and resolvent of linear operators
43A45 Spectral synthesis on groups, etc.
47B10 Operators defined by summability properties
47B38 Operators on function spaces
47A20 Extensions and related concepts of linear operators

Keywords: Gel'fand's representation theory of commutative B- and B *-algebras; Stone-Čech compactification; non-commutative B *-algebras; spectral resolution for normal operators; eigenvalues; minimax theorems; integral formula; unitary invariants of a normal operator; fixed point theorem of Kakutani; Haar measure on compact groups; Peter-Weyl theorem; Bohr compactification; Bohr's characterization of almost periodic functions; Fourier analysis on locally compact, $\sigma $-compact Abelian groups; spectral synthesis; Calderón-Zygmund and Marcinkiewicz theorems; singular convolution operators; spectral study of the compact operators belonging to a v. Neumann-Schatten ideal; Hilbert-Schmidt class; spectral resolution of self-adjoint operators; v. Neumann functional calculus with unbounded functions; extensions of a symmetric operator; Friedrichs' theorem on the extension of semi-bounded symmetric operators; Stone representation theorem; moment problems; Carleman integral operators; Bade-Schwartz represenation; spectral theory of formally self-adjoint operators made from the functional analytic point of view; Green function; deficiency indices; formally self-adjoint different operators; linear partial differential equations and operators; Gårding-Browder eigenfunction expansion theorem; Gårding inequality; Cauchy problem for symmetric hyperbolic systems; mixed problem for parapolic equations; semi-groups of operators

Citations: Zbl 0084.104; Zbl 0093.114; Zbl 0128.348

Cited in: Zbl 1116.47040 Zbl 1120.47006

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