## Linear Operators, Part 2 |

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Page 1079

Let {,u,-} be the

of decreasing absolute value. Show that llll § #11 liq}-sl § #1/lať liq}-2)~al §/41/is/

ls' etc[Remarkz This result is the best possible (Horn).] 31 (H. Weyl) Let {10} ...

Let {,u,-} be the

**eigenvalues**of B. Suppose that {)0} and {fa} are arranged in orderof decreasing absolute value. Show that llll § #11 liq}-sl § #1/lať liq}-2)~al §/41/is/

ls' etc[Remarkz This result is the best possible (Horn).] 31 (H. Weyl) Let {10} ...

Page 1383

With boundary conditions A, the

from the equation sin \/ 1. = 0. Consequently, in Case A, the

the numbers of the form (n1t)', n g1; in Case C, the numbers {(n+§)n}'*', n g 0.

With boundary conditions A, the

**eigenvalues**are consequently to be determinedfrom the equation sin \/ 1. = 0. Consequently, in Case A, the

**eigenvalues**1 arethe numbers of the form (n1t)', n g1; in Case C, the numbers {(n+§)n}'*', n g 0.

Page 1497

In the former case the matrix B(1) necessarily has an eigenvector belonging to

the

discrete

the ...

In the former case the matrix B(1) necessarily has an eigenvector belonging to

the

**eigenvalue**+1; in the latter case, ... By Theorem 64, we now see that thediscrete

**eigenvalues**of those two problems are the only possible end points inthe ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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