## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 46

Page 911

Theorem 1 may now be applied to the restriction Tx of T to the

regular

the complement of a(T)) and a unitary mapping Ua between Spa and L2(ua) ...

Theorem 1 may now be applied to the restriction Tx of T to the

**space**$x to yield aregular

**positive measure**fia vanishing on the complement of a(Ta) (and thus onthe complement of a(T)) and a unitary mapping Ua between Spa and L2(ua) ...

Page 1173

Let (S,Z,/n) be a

defined in E", homogeneous of order 0, smooth except atx = 0, and whose

surface integral over the surface of the unit sphere is zero. Let £„(£„) denote the ...

Let (S,Z,/n) be a

**positive measure space**. Let Q(x) be a numerically-valued kerneldefined in E", homogeneous of order 0, smooth except atx = 0, and whose

surface integral over the surface of the unit sphere is zero. Let £„(£„) denote the ...

Page 1210

Let T be a self adjoint operator in the Hilbert space L2(S, Z, v), where (S, Z, v) is a

that there exists an increasing sequence {Sn} covering S, each element of which

...

Let T be a self adjoint operator in the Hilbert space L2(S, Z, v), where (S, Z, v) is a

**positive measure space**. Let E be the resolution of the identity for T. We assumethat there exists an increasing sequence {Sn} covering S, each element of which

...

### 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