## Linear Operators: Spectral theory |

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Page 1191

However, this

that any function g with a continuous first derivative has the property that (#1 -(, ; *

(i. 'd *)- hijo, fe i}). and thus any such g, even though it fails to vanish at one of the

...

However, this

**operator**is not self**adjoint**for it is clear from the above equationsthat any function g with a continuous first derivative has the property that (#1 -(, ; *

(i. 'd *)- hijo, fe i}). and thus any such g, even though it fails to vanish at one of the

...

Page 1270

The problem of determining whether a given symmetric

theorem may be employed. If the answer to this problem is affirmative, it is

important to ...

The problem of determining whether a given symmetric

**operator**has a self**adjoint**extension is of crucial importance in determining whether the spectraltheorem may be employed. If the answer to this problem is affirmative, it is

important to ...

Page 1548

extensions of S and S respectively, and let A,(T) and 2,07) be the numbers

defined for the self adjoint operators T and T as in Exercise D2. Show that A, T) >

A,(T), n > 1. D11 Let T. be a self

be a ...

extensions of S and S respectively, and let A,(T) and 2,07) be the numbers

defined for the self adjoint operators T and T as in Exercise D2. Show that A, T) >

A,(T), n > 1. D11 Let T. be a self

**adjoint operator**in Hilbert space $31, and let Tobe a ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete 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 identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero