## Linear operators: Spectral operators |

### From inside the book

Results 1-3 of 87

Page 1931

The notion of "

the domain D(f) of an extension may contain points which cannot be connected

with any point in p(T) by a curve in D(f). -* 6 Definition. The function R(£\ T)x is

said ...

The notion of "

**analytic**extension" differs from that of "**analytic**continuation," forthe domain D(f) of an extension may contain points which cannot be connected

with any point in p(T) by a curve in D(f). -* 6 Definition. The function R(£\ T)x is

said ...

Page 1932

In this case x(£) is a single valued

= B(t;T)z, $eP(T). It will be shown in the next section that, if T is a spectral operator

, the function R(£; T)x has, for every x in X, the single valued extension property ...

In this case x(£) is a single valued

**analytic**function with domain p(x) and with x(i)= B(t;T)z, $eP(T). It will be shown in the next section that, if T is a spectral operator

, the function R(£; T)x has, for every x in X, the single valued extension property ...

Page 2248

Let/be a function

number of exceptional points p, includes a neighborhood of a(T) and a

neighborhood of the point at infinity. Suppose that each exceptional point p

satisfies E(p) ...

Let/be a function

**analytic**in a domain U which, when taken together with a finitenumber of exceptional points p, includes a neighborhood of a(T) and a

neighborhood of the point at infinity. Suppose that each exceptional point p

satisfies E(p) ...

### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

### Other editions - View all

### Common terms and phrases

adjoint operator algebra of projections Amer analytic arbitrary asymptotic B-space Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complex numbers complex plane constant contains continuous functions converges Corollary countably additive Definition denote dense differential operator disjoint Doklady Akad domain eigenvalues elements equation exists finite number Foias follows from Lemma follows from Theorem formal differential operator formula Hence Hilbert space hypothesis identity inequality inverse Lebesgue Math matrix measurable functions multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proof properties prove quasi-nilpotent restriction Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset Suppose trace class type spectral operator unbounded uniformly bounded unique vector weakly complete zero