## Linear Operators, Part 2 |

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Page 1120

Throughout the present section, we

space is separable. Subdiagonal representations of an operator are connected

with the study of its invariant subspaces. Thus, the key to the situation that we ...

Throughout the present section, we

**assume**for simplicity of statement that Hilbertspace is separable. Subdiagonal representations of an operator are connected

with the study of its invariant subspaces. Thus, the key to the situation that we ...

Page 1611

We

differential operator of the form [1-] on an interval which will be specified in each

case, and with the understanding that when no interval is mentioned, the result is

...

We

**assume**, unless it is otherwise stated, that 1 is a formally symmetric formaldifferential operator of the form [1-] on an interval which will be specified in each

case, and with the understanding that when no interval is mentioned, the result is

...

Page 1629

... differential operator L of order m defined in a domain D of Euclidean rt-space,

we mean a formal expression m 1| 31 (1) L=2 Z a-...,-(t1,...,t,,)i—, ,_° ,p,'_...,,,_, '* I

8l,_1...8i,.! the coefficients a,-l___,-,(t1, . . ., tn) being

... differential operator L of order m defined in a domain D of Euclidean rt-space,

we mean a formal expression m 1| 31 (1) L=2 Z a-...,-(t1,...,t,,)i—, ,_° ,p,'_...,,,_, '* I

8l,_1...8i,.! the coefficients a,-l___,-,(t1, . . ., tn) being

**assumed**to be defined for t ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY | 858 |

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 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