## Linear Operators, Part 2 |

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Results 1-3 of 44

Page 911

2.5:)“ of the Hilbert

applied to the restriction Ta of T to the

of o(T)) and ...

2.5:)“ of the Hilbert

**spaces**$5' (cf. Lemma IV.4.l9). Theorem 1 may now beapplied to the restriction Ta of T to the

**space**{pa to yield a regular**positive****measure**Ina vanishing on the complement of o(Ta) (and thus on the complementof o(T)) and ...

Page 1173

Let (S, Z',;4) be a

in an evident manner be identified with the L,-

and the inequality to be proved reduces to Q _ 1| <41) Us ix 31”.) /(y.s)dy we g c' ...

Let (S, Z',;4) be a

**positive measure**spaee. Let .Q(.2:) be a ... The**space**L,(L,) mayin an evident manner be identified with the L,-

**space**on the product set E"><Sand the inequality to be proved reduces to Q _ 1| <41) Us ix 31”.) /(y.s)dy we g c' ...

Page 1210

Let T be a self adjoint operator in the Hilbert space L2(S, Z, 11), where (S, Z, v) is

a

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

Let T be a self adjoint operator in the Hilbert space L2(S, Z, 11), 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 ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### 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 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 f Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero