## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 87

Page 1248

A bounded linear operator P in Hilbert space S) is

there is a closed subspace J such that |Prs = |a| for r in JJ' and P(W)") = {0}. The

subspace Jo is

domain ...

A bounded linear operator P in Hilbert space S) is

**called**a partial isometry ifthere is a closed subspace J such that |Prs = |a| for r in JJ' and P(W)") = {0}. The

subspace Jo is

**called**the initial domain of P and P.J. (= PS)) is**called**the finaldomain ...

Page 1297

If A(f) = 0 for each function in the domain of Ti(r) which vanishes in a

neighborhood of a, A will be

boundary value at b is defined similarly. By analogy with Definition XII.4.25 an

equation B(f) = 0, ...

If A(f) = 0 for each function in the domain of Ti(r) which vanishes in a

neighborhood of a, A will be

**called**a boundary value at a. The concept of aboundary value at b is defined similarly. By analogy with Definition XII.4.25 an

equation B(f) = 0, ...

Page 1432

In this case, v is

there is no singularity at all, and zero is

equation. If y = 1, the singularity of equation [+] at zero is

singularity ...

In this case, v is

**called**the order of the singularity of equation [+] at zero. If y = 0,there is no singularity at all, and zero is

**called**a regular point of the differentialequation. If y = 1, the singularity of equation [+] at zero is

**called**a regularsingularity ...

### 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 | |

48 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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