## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 91

Page 1188

If the domain ®(T) of the operator T is

consists, by definition, of all y in ,£> for which (Tx, y) is continuous for x in %(T).

Since 3)(T) is

such ...

If the domain ®(T) of the operator T is

**dense**in ,£) then the domain S)(7'*)consists, by definition, of all y in ,£> for which (Tx, y) is continuous for x in %(T).

Since 3)(T) is

**dense**in £> there is (IV. 4. 5) a uniquely determined point y* in ,£>such ...

Page 1271

frequently-used device, it is appropriate that we give a brief sketch indicating how

the Cayley transform can be used to determine when a symmetric operator has a

self adjoint extension. Let T be a symmetric operator with domain ^(T)

frequently-used device, it is appropriate that we give a brief sketch indicating how

the Cayley transform can be used to determine when a symmetric operator has a

self adjoint extension. Let T be a symmetric operator with domain ^(T)

**dense**in ...Page 1905

... Saks decomposition, IV.9.7 (308) Yosida-Hewitt decomposition, (233)

Deficiency indices and spaces, definition, XII.4.9 (1226) De Morgan, rules of, (2)

... Saks decomposition, IV.9.7 (308) Yosida-Hewitt decomposition, (233)

Deficiency indices and spaces, definition, XII.4.9 (1226) De Morgan, rules of, (2)

**Dense**convex sets, V.7.27 (437)**Dense**linear manifolds, V.7.40-41 (438-139)**Dense**set, ...### 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 | |

9 other sections not shown

### Other editions - View all

### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function q Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma Proc prove real axis real numbers representation satisfies Section sequence singular solution spectral spectral theory square-integrable subspace Suppose symmetric operator theory topology transform unique unitary vanishes vector zero