## Linear Operators, Part 2 |

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Page 1463

q.>/§+<p.—1».></;>= +1»./;'</1 f=—/§/1)'}Since all the terms in the integral on the

right are non-negative, we must have f; f,—f;f, identically

' = /;'</1/.-/;/.> is identically

q.>/§+<p.—1».></;>= +1»./;'</1 f=—/§/1)'}Since all the terms in the integral on the

right are non-negative, we must have f; f,—f;f, identically

**zero**in [c, d]. Thus (1. 1?)' = /;'</1/.-/;/.> is identically

**zero**in [c, d], so that f,f;1 is constant. Moreover, since ...Page 1474

Then 1.l < 1.. Since, by Lemma 35. a(t, 1.) has a

of a(t, 1.1), we have only to show that the interval (a, z] between a and the

smallest

that a(t ...

Then 1.l < 1.. Since, by Lemma 35. a(t, 1.) has a

**zero**between every pair of**zeros**of a(t, 1.1), we have only to show that the interval (a, z] between a and the

smallest

**zero**z of a(t, /ll) contains a**zero**of a(t, 1.), and we will have establishedthat a(t ...

Page 1475

If we can show that a(-, 1,) has a

established that a(-, 1,) has at least n+1

1, is in J". It is sufficient to prove that o(-, 1,) has a

If we can show that a(-, 1,) has a

**zero**in (a, zl] and a**zero**in [z,, b), we will haveestablished that a(-, 1,) has at least n+1

**zeros**in (a, b), contradicting the fact that1, is in J". It is sufficient to prove that o(-, 1,) has a

**zero**in (a, 21], for then it will ...### 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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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