## Linear Operators: Spectral theory |

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Page 1099

Since both sides of (1) are continuous in T and since every finite matrix may be

approximated arbitrarily closely by non-

consider the case in which T is non-

and if ...

Since both sides of (1) are continuous in T and since every finite matrix may be

approximated arbitrarily closely by non-

**singular**matrices, it is sufficient toconsider the case in which T is non-

**singular**. Then A = (TT")/* is also non-**singular**and if ...

Page 1184

z. v. A r-y ace A These B-spaces have been studied extensively in connection

with the theory of

CalderónZygmund type may be shown under suitable hypotheses to map

functions satisfying a ...

z. v. A r-y ace A These B-spaces have been studied extensively in connection

with the theory of

**singular**integrals.**Singular**integrals of Hilbert-CalderónZygmund type may be shown under suitable hypotheses to map

functions satisfying a ...

Page 1919

... III.1.1 (95) regular, definition, III.5.11 (137) properties, III.5.12–14 (137–138), III.

9.19–22 (170), IV.13.75 (350), IV.6.1–3 (261-265) relativization or restrictions of,

III.8 definition, o-finite, III.5.7 (136)

...

... III.1.1 (95) regular, definition, III.5.11 (137) properties, III.5.12–14 (137–138), III.

9.19–22 (170), IV.13.75 (350), IV.6.1–3 (261-265) relativization or restrictions of,

III.8 definition, o-finite, III.5.7 (136)

**singular**, III.4.12 (131) spaces of, as conjugate...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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### Common terms and phrases

adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete 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 identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero