## 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 V dt '•«)-

('•'*«)□ "*HY 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 V dt '•«)-

('•'*«)□ "*HY 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 5 respectively, and let X„(T) an£l ^n(^) De tne numbers

defined for the self adjoint operators T and T as in Exercise D2. Show that XJT) ^

Xn(f), n ^ 1. Dll Let T1 be a self

a ...

extensions of S and 5 respectively, and let X„(T) an£l ^n(^) De tne numbers

defined for the self adjoint operators T and T as in Exercise D2. Show that XJT) ^

Xn(f), n ^ 1. Dll Let T1 be a self

**adjoint operator**in Hilbert space §lt and let T2 bea ...

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### Contents

BAlgebras | 859 |

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 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