## Linear Operators: Spectral operators |

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Page 911

It is clear that we may regard Y) as the direct sum X = X \}, of the Hilbert

(cf. Lemma IV.4.19). Theorem I may now be applied to the restriction T. of T to the

It is clear that we may regard Y) as the direct sum X = X \}, of the Hilbert

**spaces**Y,(cf. Lemma IV.4.19). Theorem I may now be applied to the restriction T. of T to the

**space**XY, to yield a regular**positive measure**u, vanishing on the complement ...Page 1173

Nelson Dunford, Jacob T. Schwartz. 20 THEOREM. Let (S, 2, u) be a

homogeneous of order 0, smooth except at w = 0, and whose surface integral

over the surface ...

Nelson Dunford, Jacob T. Schwartz. 20 THEOREM. Let (S, 2, u) be a

**positive****measure space**. Let Q(x) be a numerically-valued kernel defined in E",homogeneous of order 0, smooth except at w = 0, and whose surface integral

over the surface ...

Page 1210

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

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 ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

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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