## Linear Operators, Part 2 |

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Page 1310

<p = 0

exactly one solution 1p(i, Z) of (r —}.)1p = 0

the boundary conditions at b. Pnoor. We shall show the theorem is true in each of

...

<p = 0

**square**-**integrable**at a and satisfying the boundary conditions at a, andexactly one solution 1p(i, Z) of (r —}.)1p = 0

**square**-**integrable**at b amt satisfyingthe boundary conditions at b. Pnoor. We shall show the theorem is true in each of

...

Page 1329

o = 0

exactly one solution ap(t, 1.) of (1 —l)o' = 0

boundary conditions at b. The resolvent R(}.; T) is an integral operator whose

kernel K ...

o = 0

**square**-**integrable**at a and satisfying the boundary conditions at a, andexactly one solution ap(t, 1.) of (1 —l)o' = 0

**squareintegrable**at b satisfying theboundary conditions at b. The resolvent R(}.; T) is an integral operator whose

kernel K ...

Page 1416

We therefore necessarily have f(co) = f1(c°). But this is impossible, because /(co)

= — ff“/'u>d¢ > — j/£<¢>d¢ = mo)\Ve conclude that co = 0 and that f(t) > f1(t)

throughout the interval (O, b). Because /1 is positive, and not

We therefore necessarily have f(co) = f1(c°). But this is impossible, because /(co)

= — ff“/'u>d¢ > — j/£<¢>d¢ = mo)\Ve conclude that co = 0 and that f(t) > f1(t)

throughout the interval (O, b). Because /1 is positive, and not

**square**-**integrable**, ...### 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