## Linear Operators, Part 2 |

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Page 1100

matrix with the same eigenvalues as A, the statement (3) follows from the

inequality Art»-<v1>. I/'1». ... Since the linear functional t~r is continuous on C1,

and since, as we have observed in the paragraph

AB is a ...

matrix with the same eigenvalues as A, the statement (3) follows from the

inequality Art»-<v1>. I/'1». ... Since the linear functional t~r is continuous on C1,

and since, as we have observed in the paragraph

**following Lemma**9, [A, B] —>AB is a ...

Page 1696

Hence, we can evidently suppose without loss of generality that the carrier C of F

is a compact subset of I. If I is included in a cube D, it

3.43 and 3.12 that there is a unique extension G of F to a distribution in D,,(D) ...

Hence, we can evidently suppose without loss of generality that the carrier C of F

is a compact subset of I. If I is included in a cube D, it

**follows from Lemmas**13,3.43 and 3.12 that there is a unique extension G of F to a distribution in D,,(D) ...

Page 1733

This lemma will be deduced from the

hypotheses of Lemma 19 be satisfied. and let k be an integer with p g k < 2p +m.

Then, if there exists a neighborhood V1 of Z0 such that f VII is in Il""(V1I), there

also ...

This lemma will be deduced from the

**following lemma**: 20 LEMMA. Let thehypotheses of Lemma 19 be satisfied. and let k be an integer with p g k < 2p +m.

Then, if there exists a neighborhood V1 of Z0 such that f VII is in Il""(V1I), there

also ...

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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