## Linear Operators, Part 2 |

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Results 1-3 of 53

Page 1099

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

non-

...

... in 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*)1/2 is also non-**singular**and if U = A-1 T, UU"' = A_1A2A'1...

Page 1184

suitable hypotheses to map functions satisfying a Holder condition of exponent 0

< s < 1 into functions of the same sort.

LittlewoodPaley ...

**Singular**integrals of Hilbert-Calderom Zygmund type may be shown undersuitable hypotheses to map functions satisfying a Holder condition of exponent 0

< s < 1 into functions of the same sort.

**Singular**integrals of Hardy-LittlewoodPaley ...

Page 1919

... 111.5.12-14 (187-188), l11.9.19-22 (170), 1V.18.75 (350), 1V.6.1—8 (261-205)

relativization or restrictions of, 111.8 n-finite, ll1.5.7 (180)

spaces of, as conjugate spaces, 1\'.5.1 (258), 1V.5.8 (259), l\'.6.2 -8 (262-264), ...

... 111.5.12-14 (187-188), l11.9.19-22 (170), 1V.18.75 (350), 1V.6.1—8 (261-205)

relativization or restrictions of, 111.8 n-finite, ll1.5.7 (180)

**singular**, 1l1.4.12 (181)spaces of, as conjugate spaces, 1\'.5.1 (258), 1V.5.8 (259), l\'.6.2 -8 (262-264), ...

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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