## Linear Operators: Spectral theory |

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Results 1-3 of 83

Page 1303

Clearly B(f) = 0 for those / which vanish in a

boundary value for x at a. To prove the converse, let B be a boundary value at a.

Choose a function h in C°°(/) which is identically equal to one in a

of a ...

Clearly B(f) = 0 for those / which vanish in a

**neighborhood**of a. Thus B is aboundary value for x at a. To prove the converse, let B be a boundary value at a.

Choose a function h in C°°(/) which is identically equal to one in a

**neighborhood**of a ...

Page 1656

Let k be an integer and let F be a distribution in I. (i) If each point p in I has a

compact and each point p in I has a

...

Let k be an integer and let F be a distribution in I. (i) If each point p in I has a

**neighborhood**Up contained in I such that F\VpeAw{UP), then F e ATM(I). (ii) If I iscompact and each point p in I has a

**neighborhood**U9 such that F\UpIeIHk){Uvl),...

Page 1733

Q.E.D. Lemma 18 enables us to use the method of proof of Theorem 2 in the

out in the next two lemmas. 19 Lemma. Let a be an elliptic formal partial

differential ...

Q.E.D. Lemma 18 enables us to use the method of proof of Theorem 2 in the

**neighborhood**of the boundary of a domain with smooth boundary. This is carriedout in the next two lemmas. 19 Lemma. Let a be an elliptic formal partial

differential ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

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### Common terms and phrases

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