## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

### From inside the book

Results 1-3 of 71

Page 1179

**PROOF**. We saw in the course of proving Theorem 25 that the mapping M K which sends a scalar - valued function with the Fourier transform f ( 5 ) into the vector - valued function whose nth component has the Fourier transform ( 5 ) ...Page 1724

**Proof**. By the preceding lemma and by Corollary 11 it suffices to show that ( Tj , g ) = ( 1 , Sg ) forf in D ( T ) and g in D ( S ) . By Green's formula , proved in the last paragraph of Section 2 , this equation is valid if | and g ...Page 1750

We shall see , however , that this fact is needed in the course of the

We shall see , however , that this fact is needed in the course of the

**proof**of Theorem 1 , and shall prove it by a direct method where it is needed . Remark 2. The theorem is false if no boundedness restriction is imposed on the ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

37 other sections not shown

### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero