## Linear Operators: Spectral theory |

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Page 1099

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

Then A = (TT*)1/2 is also non-

then U is ...

... 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~x T, UU* = A~1A2A^1 = I,then U is ...

Page 1584

The contemporary research of Hellinger [1], E. Schmidt [1, 2] and Hilbert [1] on

integral equations naturally led to an interest in a similar approach to differential

operators whose coefficients are

The contemporary research of Hellinger [1], E. Schmidt [1, 2] and Hilbert [1] on

integral equations naturally led to an interest in a similar approach to differential

operators whose coefficients are

**singular**at one or both of the endpoijits of the ...Page 1919

1.1 (95) regular, definition, III. 5. 11 (137) properties, II 1.5.12-14 (137-138), III.

9.19-22 (170), IV.13.75 (350), IV.6.1-8 (261-265) relativization or restrictions of, III

. 8 (T-finite, III.5.7 (136)

1.1 (95) regular, definition, III. 5. 11 (137) properties, II 1.5.12-14 (137-138), III.

9.19-22 (170), IV.13.75 (350), IV.6.1-8 (261-265) relativization or restrictions of, III

. 8 (T-finite, III.5.7 (136)

**singular**, HI.4.12 (131) spaces of, as conjugate spaces, ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

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 constant 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 q Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma Proc prove real axis real numbers representation satisfies Section sequence singular solution spectral spectral theory square-integrable subspace Suppose symmetric operator theory topology transform unique unitary vanishes vector zero