Linear operators. Part II: Spectral theory, self adjoint operators in Hilbert space. With the assistance of William G. Bade and Robert G. Bartle. Repr. of the orig., publ. 1963 by John Wiley & Sons Ltd., Paperback ed.

*(English)*Zbl 0635.47002
Wiley Classics Library. New York etc.: John Wiley & Sons Ltd./Interscience Publishers, Inc. ix, 859-1923 $25.95 (1988).

For a review on the original edition see Zbl 0128.348.

##### MSC:

47-02 | Research exposition (monographs, survey articles) pertaining to operator theory |

47B15 | Hermitian and normal operators (spectral measures, functional calculus, etc.) |

47F05 | General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX) |

47B25 | Linear symmetric and selfadjoint operators (unbounded) |

46J05 | General theory of commutative topological algebras |

22B05 | General properties and structure of LCA groups |

47D03 | Groups and semigroups of linear operators |

47E05 | General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX) |

47A10 | Spectrum, resolvent |

43A45 | Spectral synthesis on groups, semigroups, etc. |

47B10 | Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) |

47B38 | Linear operators on function spaces (general) |

47A20 | Dilations, extensions, compressions 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
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\textit{N. Dunford} and \textit{J. T. Schwartz}, Linear operators. Part II: Spectral theory, self adjoint operators in Hilbert space. With the assistance of William G. Bade and Robert G. Bartle. Repr. of the orig., publ. 1963 by John Wiley \& Sons Ltd., Paperback ed. New York etc: John Wiley \&| Sons Ltd./Interscience Publishers, Inc. (1988; Zbl 0635.47002)