## Linear Operators: Spectral theory |

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Page 1310

Then the boundary conditions are real , and there is exactly one solution p ( t , 2 )

of ( 1 – 2 ) 9 = 0

a , and exactly one solution y ( t , 2 ) of ( 1 - 2 ) y = 0

Then the boundary conditions are real , and there is exactly one solution p ( t , 2 )

of ( 1 – 2 ) 9 = 0

**square**-**integrable**at a and satisfying the boundary conditions ata , and exactly one solution y ( t , 2 ) of ( 1 - 2 ) y = 0

**square**-**integrable**at b ...Page 1329

Then the boundary conditions are real , and there is exactly one solution o ( t , 2 )

of ( 7 - 2 ) 0 = 0

a , and exactly one solution y ( t , 2 ) of ( 1 - 2 ) 0 = 0

Then the boundary conditions are real , and there is exactly one solution o ( t , 2 )

of ( 7 - 2 ) 0 = 0

**square**-**integrable**at a and satisfying the boundary conditions ata , and exactly one solution y ( t , 2 ) of ( 1 - 2 ) 0 = 0

**squareintegrable**at b ...Page 1552

( b ) If Q ( t ) + - 00 , Q is monotone decreasing for sufficiently large t , 1 [ g ' ( t ) ] 2

| | sq ' ( t ) 1 A l Lig ( t ) | 3 / 2 ] 49 ( t ) / 5 / 2 dt ... G2 ( Wintner ) Suppose that the

operator t has the property that whenever f is a

...

( b ) If Q ( t ) + - 00 , Q is monotone decreasing for sufficiently large t , 1 [ g ' ( t ) ] 2

| | sq ' ( t ) 1 A l Lig ( t ) | 3 / 2 ] 49 ( t ) / 5 / 2 dt ... G2 ( Wintner ) Suppose that the

operator t has the property that whenever f is a

**square**-**integrable**solution of the...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero