## Linear Operators: Spectral operators |

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Page 1099

... T and since every finite matrix may be approximated arbitrarily closely by non-

Then A = (TT*)” is also non-

...

... T and since every finite matrix may be approximated arbitrarily closely by non-

**singular**matrices, it is sufficient to consider the case in which T is non-**singular**.Then A = (TT*)” is also non-

**singular**and if U = A-1 T, UU+ = A-A*A-1 = I, then U is...

Page 1184

z. v. A r-y are 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 are 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.5 measure, III.4.3 (126) positive, 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 o-finite, III.5.7 (136)

...

... III.5 measure, III.4.3 (126) positive, 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 o-finite, III.5.7 (136)

**singular**, III.4.12 (131)...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

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### Common terms and phrases

adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero