## Linear Operators, Part 2 |

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Page 1472

least one such

ta = ha satisfy B. By the remark (a) made above, it then follows that for any two ...

least one such

**solution**must exist. On the other hand, if two linearly independent**solutions**of to = 2.0 satisfy the boundary condition B, it follows that all**solutions**ofta = ha satisfy B. By the remark (a) made above, it then follows that for any two ...

Page 1521

Putting yo = 1/2+i so that lo = l+i, we sec that the equation (L1—}.0)/ has one

oo. The

.

Putting yo = 1/2+i so that lo = l+i, we sec that the equation (L1—}.0)/ has one

**solution**of the order of t'1-" as t —> oo and another which behaves like t' as t —>oo. The

**solution**at 10 = l—i is exactly similar. Thus, by Theorem XII.4-.19, L1——}.

Page 1529

Then in this angle any

the factor exp (§§“z"“1) is exponentially small (as |z| —> oo in the angle) relative

to any

Then in this angle any

**solution**of Lf = 0 whose asymptotic expansion begins withthe factor exp (§§“z"“1) is exponentially small (as |z| —> oo in the angle) relative

to any

**solution**whose asymptotic expansion begins with the factor exp (Q';“z"'1).### What people are saying - Write a review

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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