## 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 and thus

any such g, even though it fails to vanish at one of the endpoints 0 or 1, is in 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 and thus

any such g, even though it fails to vanish at one of the endpoints 0 or 1, is in 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

T&2, x e <&{T). Show that the

is bounded below if and only if both T1 and T2 are bounded below. Let Xn(Tx), X„

(T2), and X„(T) be the numbers defined in Exercise D2, for the operators Tlt T2, ...

T&2, x e <&{T). Show that the

**operator**T is self**adjoint**. Show that the**operator**Tis bounded below if and only if both T1 and T2 are bounded below. Let Xn(Tx), X„

(T2), and X„(T) be the numbers defined in Exercise D2, for the operators Tlt T2, ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra 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 g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive 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