## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 90

Page 2088

Show that if As is a scalar type spectral operator whose spectrum lies in a left half

plane then it is the infinitesimal generator of the strongly continuous semi - group

T ( t ) , t 20 ,

Show that if As is a scalar type spectral operator whose spectrum lies in a left half

plane then it is the infinitesimal generator of the strongly continuous semi - group

T ( t ) , t 20 ,

**given**by the equation T ( t ) o e " Eda ) , O ( AS ) QEHP , where E ...Page 2096

Another characterization of subscalar operators is

which asserts that , under certain ... X 2 X which has a continuous projection onto

X . A second proof of this latter result is

Another characterization of subscalar operators is

**given**, based on a theoremwhich asserts that , under certain ... X 2 X which has a continuous projection onto

X . A second proof of this latter result is

**given**in Ionescu Tulcea and Plafker [ 1 ] .Page 2376

Applications of this same method to other operators are

Section 5 . In Section 3 we generalize the Friedrichs technique to operators with

discrete spectra , along lines first developed by Turner . Here one begins with an

...

Applications of this same method to other operators are

**given**as exercises inSection 5 . In Section 3 we generalize the Friedrichs technique to operators with

discrete spectra , along lines first developed by Turner . Here one begins with an

...

### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

9 other sections not shown

### Other editions - View all

### Common terms and phrases

adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniform uniformly unique valued vector weakly zero