## Linear Operators, Part 2 |

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Page 1187

Just as in the case of a

is defined to be the set of all complex numbers 1. such that (U —T)“1 exists as an

everywhere defined

Just as in the case of a

**bounded operator**the resolvent set p(T) of an operator Tis defined to be the set of all complex numbers 1. such that (U —T)“1 exists as an

everywhere defined

**bounded operator**. For 1 in p(T) the symbol R(}.; T) will be ...Page 1190

Q.E.D. Most of the considerations in this chapter and the next will be directed

towards an operator which is either symmetric ... Even though symmetry and self

adjointness are the same for

operator ...

Q.E.D. Most of the considerations in this chapter and the next will be directed

towards an operator which is either symmetric ... Even though symmetry and self

adjointness are the same for

**bounded operators**, an unbounded symmetricoperator ...

Page 1273

Weyl [5] showed this to be the case for differential

that the inverse

T) is ...

Weyl [5] showed this to be the case for differential

**operators**. If T is a linear**operator**with dense domain, let 1/(T) be the set of all complex numbers 1. suchthat the inverse

**operator**(T—1I)-1 exists and is**bounded**on its domain. The set y(T) is ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

13 other sections not shown

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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