## Linear Operators, Part 2 |

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Page 1656

Let k be an integer and let F be a distribution in I. (i) 1/ each point p in I has a

compact and each point p in I has a

then ...

Let k be an integer and let F be a distribution in I. (i) 1/ each point p in I has a

**neighborhood**U, contained in I such that F|U, e A"'*(U,,), then F e A""(I). (ii) I / I iscompact and each point p in I has a

**neighborhood**L', such that F|U,IeH""(U,I),then ...

Page 1678

Let 1;? be a second function in Co (I) such that 1/3(1) = 1 for .1; in a

vanishes in a

K. Hence ...

Let 1;? be a second function in Co (I) such that 1/3(1) = 1 for .1; in a

**neighborhood**of K1. Then yxp—¢<p vanishes in a**neighborhood**of K n C(F), andvanishes in a

**neighborhood**of C(F)—K since mp vanishes in the complement ofK. Hence ...

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 o 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 o be an elliptic formal partial

differential ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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