## Linear Operators: Spectral operators |

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Page 1210

Let T be a self adjoint operator in the Hilbert space L2(S, X, y), where (S, X, v) is a

positive

and that for bounded sets e the range of E(e) contains only functions which ...

Let T be a self adjoint operator in the Hilbert space L2(S, X, y), where (S, X, v) is a

positive

**measure space**. ... covering S, each element of which has finite measure,and that for bounded sets e the range of E(e) contains only functions which ...

Page 1900

Almost periodic functions, definition, IV.2.25 (242) space of, additional properties,

IV.15 (379) definition, IV.2.25 (242) ... (266) remarks concerning, (382) Atom, in a

Almost periodic functions, definition, IV.2.25 (242) space of, additional properties,

IV.15 (379) definition, IV.2.25 (242) ... (266) remarks concerning, (382) Atom, in a

**measure space**, IV.9.6 (308) Automorphisms, in groups, (35) B B-algebra.Page 1913

(See Decomposition) * * determined by a function, (142), (144) o differentiation of

, III.12 .3 change of, III.10.8 (182), X.I (894) definition, III.4.3 (126) Haar, V.11.22–

23 (460) Hausdorff 2-, III.9.47 (174) Metrization, of a

...

(See Decomposition) * * determined by a function, (142), (144) o differentiation of

, III.12 .3 change of, III.10.8 (182), X.I (894) definition, III.4.3 (126) Haar, V.11.22–

23 (460) Hausdorff 2-, III.9.47 (174) Metrization, of a

**measure space**, III.7.1 (158)...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

52 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero