## Linear Operators: Spectral theory |

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Page 1217

Two ordered representations U and Ở of H relative to T and †

measures u and ù , and multiplicity sets { en } and { ēn } will be called equivalent

if u zû and ule , 4ěn ) = 0 = ūle 4ěn ) for n = 1 , 2 , .... 16 THEOREM . A separable

...

Two ordered representations U and Ở of H relative to T and †

**respectively**, withmeasures u and ù , and multiplicity sets { en } and { ēn } will be called equivalent

if u zû and ule , 4ěn ) = 0 = ūle 4ěn ) for n = 1 , 2 , .... 16 THEOREM . A separable

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Page 1326

for all solutions of ( 1-2 ) 0 = 0 ( ( 7 * —ā ) 0 = 0 ) which are squareintegrable in a

neighborhood of a and b

at a and at b

for all solutions of ( 1-2 ) 0 = 0 ( ( 7 * —ā ) 0 = 0 ) which are squareintegrable in a

neighborhood of a and b

**respectively**, and which satisfy the boundary conditionsat a and at b

**respectively**. Then the resolvent R ( 2 ; T ) = ( 21 - T ) -1 is given by ...Page 1548

extensions of S and Ŝ

defined for the self adjoint operators T and Î as in Exercise D2 . Show that an ( T )

22n ( † ) , n 2 1 . D11 Let T , be a self adjoint operator in Hilbert space Hi , and let

...

extensions of S and Ŝ

**respectively**, and let 2n ( T ) and an ( Î ) be the numbersdefined for the self adjoint operators T and Î as in Exercise D2 . Show that an ( T )

22n ( † ) , n 2 1 . D11 Let T , be a self adjoint operator in Hilbert space Hi , and let

...

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Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

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