## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 79

Page 1179

Theorem 25 remains valid in the full range 1 < p < 0 . a

Theorem 25 remains valid in the full range 1 < p < 0 . a

**PROOF**. We saw in the course of proving Theorem 25 that the mapping MX which sends a scalar - valued function with the Fourier transform f ( ) into the vector - valued function ...Page 1724

0 a

0 a

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

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

13 other sections not shown

### Other editions - View all

### Common terms and phrases

additive Akad 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 given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero